Publication List

Publications in Refereed Journals:

    Papers accepted

  1. (with Bin Deng and Liming Sun) Sharp quantitative estimates of Struwe's Decomposition Duke Mathematical Journal accepted for publication.
  2. (with Juan Davila, Manuel del Pino and Monica Musso) Leapfrogging vortex rings for the 3-dimensional incompressible Euler equations Comm. Pure Appl. Math. accepted for publication.
  3. (with Yong Liu, Kelei Wang and Ke Wu) On Dancer's conjecture for stable solutions with sign-changing nonlinearity Proc. American Math. Soc. accepted for publication.
  4. (with Bin Deng and Liming Sun) Quantitative stability of harmonic maps from $R^2$ to $S^2$ with higher degree Cal. Var. Partial Differential Equations accepted for publication.
  5. (with M. Li, X. Luo and M. Zhen) Free and harmonic trapped spin-1 Bose-Einstein condensates in $\mathbb{R}^{3}$ SIAM J. Math. Analysis accepted for publication.
  6. (with Tuoxin Li and Zikai Ye) On Sharp Beckner's Inequality for Axially Symmetric Functions on $\mathbb{S}^4$ Math Research Letters accepted for publication.
  7. (with L. Cai, J. Wang and W. Yang) Infinite time bubble towers in the fractional heat equation with ciritical exponent Annali della Scuola Normale Superiore di Pisa, Classe di Scienze accepted for publication
  8. (with Y. Liu, X. Ma and W. Wu) Entire solutions of the magnetic Ginzburg-Landau equation in $\mathbb{R}^4$ Annali della Scuola Normale Superiore di Pisa, Classe di Scienze accepted for publication

    9. 2024

  9. (with Joao H. Andrade and Zikai Ye) Complete metrics with constant fractional higher order Q-curvature on the punctured sphere Journal of Geometric Analysis 34 (2024), no. 1, 6.
  10. (with Teresa D'Aprile and Lei Zhang) On the construction of non-simple blow-up solutions for the singular Liouville equation with a potential Cal. Var. Partial Differential Equations 63 (2024), no. 3, Paper No. 68.
  11. (with Teresa D'Aprile and Lei Zhang) Non-simple blowup for singular Liouville equations in unit ball Discrete Contin. Dyn. Syst.-A 44(2024), no. 7, 1938-1957.
  12. (with Daniel Gomez, Markus Medeiros and Wen Yang) Spike solutions to the supercritical fractional Gierer-Meinhardt system Journal of Nonlinear Sciences 34(2024), no.1, Paper No. 24, 57pp.
  13. (with F. Kong and C. Lai) Global existence and aggregation of chemotaxis-fluid systems in dimension two Journal of Differential Equations 400(2024), 1-89.
  14. (with F. Kong and M. Ward) Existence, Stability and Slow Dynamics of Spikes in a 1D Minimal Keller–Segel Model with Logistic Growth Journal of Nonlinear Sciences 34(2024), no.3, Paper No. 51
  15. (with Tuoxin Li and Yuanze Wu) Infinitely many nonradial positive solutions for multi-species nonlinear Schr\"odinger systems in $R^N$ Journal of Diff. Eqns. 381(2024), 340-396.
  16. (with Ke Wu) A Liouville theorem for superlinear parabolic equations on the Heisenberg group Advance Nonlinear Studies (special volume in honor of Joel Spruck) 24(2024), no.1, Paper No. 189
  17. (with Qidi Zhang and Yifu Zhou) On Fila-King Conjecture in dimension four Journal of Diff. Eqns. 398 (2024), 38–140

    18. 2023

  18. (with L. Cui, W. Yang and L. Zhang) The blow-up analysis on $B_2^{(1)}$ affine Toda system: local mass and affine Weyl group WEYL GROUP International Mathematics Research Notices 2023, no. 18, 16140–16199.
  19. (with Bin Deng and Liming Sun) Non-degeneracy and quantitative stability of half-harmonic maps from $\R$ to $\S$ Advances in Math 420 (2023), Paper No. 108979, 42 pp.
  20. (with Daniel Gomez and Zhangyu Yang) Multi-spike solutions to the one-dimensional subcritical fractional Schnakenberg system Physica D: Nonlinear Phenomena 448 (2023), Paper No. 133720, 12 pp.
  21. (with V. Guan and M. Murugan) Helmholtz Solutions for the Fractional Laplacian and Other Related Operators Commun. Contemp. Math. 25 (2023), no. 2, Paper No. 2250016, 18 pp.
  22. (with F. Kong) Existence and Stability of Localized Patterns in the Population Models with Large Advection and Strong Allee Effect SIAM Journal of Math Analysis 55 (2023), no. 4, 2505–2552
  23. (with F. Kong and L. Xu) The Existence and Stability of Spikes in the One-dimensional Keller-Segel model with logistic growth Journal of Mathematical Biology 86 (2023), no. 1, Paper No. 6.
  24. (with F. Kong and L. Xu) Existence of Multi-spikes in the Keller-Segel model with logistic growth Math. Models Methods Appl. Sci. (Special Volume on Chemotaxis) 33 (2023), no. 11, 2227–2270.
  25. (with C. Lai and Y. Zhou) Global existence of free-energy solutions to the 2D Patlak--Keller--Segel--Navier--Stokes system with critical and subcritical mass Indiana Univ. Math. J. 72 (2023), no. 1, 43–87.
  26. (with Houwang Li and Wenming Zou) Uniqueness, multiplicity and nondegeneracy of positive solutions to the Lane-Emden problem J. Math. Pures Appl. (9) 179 (2023), 1–67
  27. (with FHLin, Y. Sire and Y. Zhou) Nematic liquid crystal flow with partially free boundary Arch. Rat. Mech. Anal. 247 (2023), no. 2, 20
  28. (with Xin Yang Lu) Uniform bound on the number of partitions for optimal configurations of the Ohta-Kawasaki energy in 3D Canadian Mathematical Bulletin Volume 66 , Issue 4 , December 2023 , pp. 1341 - 1353
  29. (with Senping Luo) On minima of difference of theta functions and application to hexagonal crystallization Math Annalen 387 (2023), no. 1-2, 499–539.
  30. (with D. E. Pelinovsky and Yuanze Wu) Positive solutions of the Gross--Pitaevskii equation for energy critical and supercritical nonlinearities Nonlinearity 36 (2023), no. 7, 3684–3709.
  31. (with X. Ren) The BCC lattice in a long range interaction system SIAM J. Appl. Math. 83 (2023), no. 5, 1854–1871.
  32. (with Y. Sire and Y. Zheng) Singularity formation in the harmonic map flow with free boundary American Journal of Mathematics 145 (2023), no. 4, 1273–1314.
  33. (with Ke Wu) On singular solutions of Lane-Emden equation on the Heisenberg group Advance Nonlinear Studies 23 (2023), no. 1, ans–2023–0084
  34. (with N. Wu and L. Zhang) Estimates of bubbling solutions of $SU(3)$ Toda systems at critical parameters-Part 2 Journal of London Math. Society 107 (2023), no. 6, 2150–2196
  35. (with Yuanze Wu) On some nonlinear Schr\"odinger equations in $R^N$ Proceedings of the Royal Society of Edinburgh Section A: Mathematics 153 (2023), no. 5, 1503–1528.

    36. 2022

  36. (with WW Ao, M. Gonzalez and A. Hyder ) Removability of singularities and maximum principles for some fractional Laplacian equations Indiana Univ. Math. Journal 71 (2022), no. 2, 735–766.
  37. (with WW Ao and Yong Liu) Clustered travelling vortex rings to the axisymmetric three-dimensional incompressible Euler flows Physica D--Nonlinear Phenomena 434(2022), Paper No. 133258
  38. (with Juan Davila, Manuel del Pino and Monica Musso) Travelling helices and the vortex filament conjecture in the incompressible Euler equations Calc. Var. Partial Differential Equations 61(2022), n0.4, 119
  39. (with Daniel Gomez and Linfeng Mei) Boundary layer solutions in the Gierer-Meinhardt system with mixed inhomogeneous boundary conditions Physica D: Nonlinear Phenomena 429 (2022), Paper No. 133071.
  40. (with Daniel Gomez and Wen Yang) Stability of spike solutions to the fractional Gierer-Meinhardt system in a one-dimensional domain Numer. Math. Theory Methods Appl. 15 (2022), no. 4, 938–989.
  41. (with C. Lai, F. Lin, C. Wang and Y. Zhou) Finite time blow-up for the nematic liquid crystal flow in dimension two Comm. Pure Appl. Math 75(2022), no.1, 128-196.
  42. (with Z. Liu and J. Zhang) A new type of nodal solutions to a singularly perturbed elliptic equations with supercritical growth J. Diff. Eqns. J. Differential Equations 339 (2022), 509–554.
  43. (with Yong Liu) A complete classification of finite Morse index solutions to elliptic sine-Gordon equation in the plane Revista Matemαtica Iberoamericana 38(2022), no.2, 355-432.
  44. (with Yong Liu, Kelei Wang and Ke Wu) Qualitative properties of stable solutions to some supercritical problems Electronic Research Archive (special volume for Dancer) 30(2022), no.5, 1668-1690.
  45. (with SP Luo) On minima of sum of theta functions and Mueller-Ho Conjecture Arch Rational Mech Analysis 243 (2022), no. 1, 139–199
  46. (with SP Luo and WM Zou) Monotonicity formula and classification of stable solutions to polyharmonic Lane-Emden equations International Mathematics Research Notices 2022, no. 21, 16902–16953.
  47. (with X.Luo, X. Yang and M. Zhen) Normalized solutions for Schr\"{o}dinger system with quadratic and cubic interactions Journal of Differential Equations 314 (2022), 56–127.
  48. (with Markus Medeiros and Wen Yang) Existence and stability of symmetric and asymmetric ppatterns for the half-Laplacian Gierer-Meinhardt system in on-dimensional domain Math. Models Methods Appl. Sci. 32 (2022), no. 6, 1193–1250
  49. (with Y. Sire and Y. Zheng) Extinction behaviour for the fast diffusion equations with critical exponent and Dirichlet boundary conditions Journal of London Math Society 106 (2022), no. 2, 855–898.
  50. (with L. Sun and Q. Zhang) Bubble towers in the ancient solution of energy-critical heat equation Cal. Var. PDE 61 (2022), no. 6, Paper No. 200, 47 pp.
  51. (with Ke Wu) Local behavior of solutions to a fractional equation with isolated singularity and critical Serrin exponent DCDS-A 42 (2022), no. 8, 4031–4052
  52. (with Yuanze Wu) Normalized solutions for Schr\"odinger equations with critical Sobolev exponent and mixed nonlinearities Journal of Functional Analysis 283 (2022), no. 6, Paper No. 109574.
  53. (with Yuanze Wu) On the stability of Caffarelli-Kohn-Nirenberg inequality Math Annalen 384 (2022), no. 3-4, 1509–1546.
  54. (with Lei Zhang) Vanishing Estimates for Liouville equation with quantized singularities Proc. London Math. Soc. 124 (2022), no. 1, 106–131.
  55. (with Qidi Zhang and Yifu Zhou) On the parabolic gluing method and singularity formation C. R. Math. Rep. Acad. Sci. Canada Vol. 44 (4) 2022, pp. 69–87
  56. (with W. Zou and X. Zhong) On Sirakov's open problem and related topics Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 23 (2022), no. 2, 959–992.

    57. 2021

  57. (with WW Ao, Juan Davila, Manuel del Pino and Monica Musso) Travelling and rotating solutions to the generalized inviscid surface quasi-geostrophic equation Trans. Amer. Math. Soc. 374 (2021), no. 9, 6665–6689.
  58. (with WW Ao, Y. Huang and Yong Li) Generalized Adler-Moser polynomials and multiple vortex rings for the Gross-Pitaevskii equation SIAM J. Math. Anal. 53 (2021), no. 6, 6959–6992.
  59. (with B. Deng, Y. Sire and K. Wu) Classification of Blow-ups and Monotonicity Formula for Half Laplacian Nonlinear Heat Equation Calc. Var. Partial Differential Equations 60 (2021), no. 1, 52.
  60. (with Manuel del Pino and Monica Musso) Geometry driven Type II higher dimensional blow-up for the critical heat equation Journal of Functional Analysis 280 (2021), no. 1, 108788.
  61. (with Manuel del Pino and Monica Musso) Existence and stability of infinite time bubble towers in the energy critical heat equation Analysis & PDE 14 (2021), no. 5, 1557–1598.
  62. (with Daniel Gomez) Multi-spike pattern in the Gierer-Meinhardt system with a non-zero activator boundary flux Journal of Nonlinear Science 31 (2021), no. 2, 37.
  63. (with D. Gomez and L. Mei) Hopf bifurcations from spike solutions for the weak coupling Gierer-Meinhardt system European Journal of Applied Mathematics 32 (2021), no. 1, 113–145.
  64. (with Daniel Gomez and Michael Ward) An Asymptotic Analysis of Localized 3-D Spot Patterns for the Gierer-Meinhardt Model: Existence, Linear Stability and Slow Dynamics SIAM J. Appl. Math. 81 (2021), no. 2, 378–406.
  65. (with F. Hamel, Y. Liu, P. Sicbaldi and K. Wang) Half-space theorems for the Allen-Cahn equation and related problems Journal fur die Reine und Angew. Math. (Crelle's Journal) 770 (2021), 113–133.
  66. (with S.Kim and M. Musso) A compactness theorem of the fractional Yamabe problem, Part I: the non-umbilic conformal infinity Journal of European Math Society 23 (2021), no. 9, 3017–3073.
  67. (with S.Kim and M. Musso) Compactness of scalar-flat conformal metrics on low-dimensional manifolds with constant mean curvature on boundary Ann. Inst. H. Poincarι Anal. Non Linιaire 38 (2021), no. 6, 1763–1793
  68. (with Yong Liu and Kelei Wang) On smooth solutions to one phase free boundary problem in $R^n$ International Mathematics Research Notices (IMRN) 2021, no. 20, 15682–15732.
  69. (with P. Luo, S. Peng and S. Yan) Excited states of Bose-Einstein condensates with degenerate attractive interactions CVPDE 60 (2021), no. 4, Paper No. 155
  70. (with SP Luo and C. Wang) On the regular part of Bloch Green function: analytical formula and critical points Analysis and Mathematical Physics 11 (2021), no. 2, 94.
  71. (with SP Luo and WM Zou) Decomposition of polyharmonic operator and classification of Homogeneous stable solutions Proc. Ameri. Math. Soc. 149 (2021), no. 7, 2957–2968.
  72. (with Slim Ibrahim, Hiroaki Kikuchi and Kenji Nakanishi) Non-uniqueness for an energy-critical heat equation on $\R^2$ Math Annalen 380 (2021), no. 1-2, 317–348.
  73. (with Y. Sire and Y. Zheng) Infinite time blow-up for half-harmonic map flow from $\mathbb{R}$ into $\mathbb{S}^1$ American Journal of Mathematics 143(2021), no.4, 1261-1335.
  74. (with Yuanze Wu) Infinitely many vortex solutions of the magnetic Ginzburg-Landau equation with external potentials in $R^2$ Journal of Mathematical Physics 62 (2021), no. 4, 041509, 33 pp.
  75. (with Lei Zhang) Estimates for Liouville equation with quantized singularities Advances in Mathematics 380 (2021), 107606.
  76. (with Maoding Zhen) Classification of positive ground state solutions with different Morse indices for nonlinear $N$-coupled Schr\"{o}dinger system Analysis in Theory and Applications (special volume in honor of P. Rabinowitz's 80th birthday) 37 (2021), no. 2, 230–266.

    77. 2020

  77. (with W. Ao, Azahara Delatorre and Mar Gonzalez) A gluing approach for the fractional Yamabe problem with isolated singularities Journal fur die Reine und Angew. Math. (Crelle's Journal) 2020, no. 763, 25–78.
  78. (with WW Ao, H. Chan, A. Delatorre, M. Fontelos, M. Gonzalez) ODE methods in non-local equations Journal of Mathematical Study, A special volume for Prof. A. Chang's 70th birthday 53 (2020), no. 4, 370–401.
  79. (with T. D'Aprile) Bubbling solutions for the Liouville equation with a singular source: non-simple blow-up Journal of Functional Analysis 279 (2020), no. 6, 108605.
  80. (with W. Ao, H. Chan, Mar Gonzalez) Bound state solutions for the supercritical fractional Schrodinger equation Nonlinear Analysis (special issue) 193(2020), 111448.
  81. (with WW Ao and M. Winter) Stable spike clusters on a compact two-dimensional Riemannian manifold Journal of Differential Equations 268 (2020), no. 7, 3665–3704.
  82. (with Andreas Buttenschoen, Theodore Kolokolnikov, and Michael Ward ) Cops-on-the-Dots: The Linear Stability of Crime Hotspots for a 1-D Reaction-Diffusion Model of Urban Crime European J. Appl. Math. 31 (2020), no. 5, 871–917.
  83. (with G. Chen and Y.Zhou) Finite time blow ups for fractional critical heat equations Nonlinear Analysis (special issue) 193(2020), 111420.
  84. (with G. Chen and Y.Liu) Nondegeneracy of harmonic maps from $\mathbb R^2$ to $\mathbb S^2$ DCDS-A (special issue on Wei-Ming Ni's 70th birthday) 40 (2020), no. 6, 3215–3233.
  85. (with Juan Davila, Manuel del Pino and Monica Musso) Gluing methods for vortex dynamics in Euler equation Arch Rational Mech Anal 235 (2020), no. 3, 1467–1530.
  86. (with Manuel del Pino, Monica Musso and Y. Zheng) Sign-changing blowing-up solutions for the critical nonlinear heat equation Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 21 (2020), 569–641
  87. (with Manuel del Pino and Juan Davila) Singularity formation for the two-dimensional harmonic map flow into $S^2$ Singularity formation for the two-dimensional harmonic map flow into $S^2$ (full version) Inventione Mathematicae 219 (2020), no.2, 345–466.
  88. (with Manuel del Pino and Monica Musso) Infinite time blow-up for the three dimensional energy critical heat equation Analysis &PDE 13 (2020), no. 1, 215–274.
  89. (with Manuel del Pino, Monica Musso and Y. Zhou) Type II finite time blow-up for the energy critical heat equation in $\mathbb{R}^4$ DCDS-A (special volume for W.-M. Ni's 70th birthday) 40 (2020), no. 6, 3327–3355
  90. (with D. Gomez and L. Mei) Stable and unstable periodic spiky solutions for the Gray-Scott system and the Schnakenberg system J. Dynam. Differential Equations 32 (2020), no. 1, 441–481.
  91. (with C. Gui and K. Wang) Axially symmetric solutions of Allen-Cahn equation with finite Morse index Transc. Amer. Math. Soc. 373 (2020), no. 5, 3649–3668.
  92. (with ZM Guo, X. Huang and LP Wang) On Delaunay solutions of a biharmonic elliptic equation with critical exponent Journal d'Analyse Mathematique 140 (2020), no. 1, 371–394.
  93. (with A. Hyder and Chang-Shou Lin) On $SU(3)$ Toda system with multiple singular sources Pacific Journal of Mathematics 305 (2020), no. 2, 645–666.
  94. (with A. Hyder and Wen Yang) On the general Toda system with multiple singular sources Cal. Var. PDE 59 (2020), no. 4, Paper No. 136, 19 pp.
  95. (with T. Kolokolnikov) Hexagonal spike clusters for some PDE's in 2D Discrete Contin. Dyn. Syst. Ser. B 25 (2020), no. 10, 4057–4070
  96. (with Yong Liu) Multi-vortex traveling waves for the Gross-Pitaevskii equation and the Adler-Moser polynomials SIAM Journal of Mathematical Analysis 52 (2020), no. 4, 3546–3579
  97. (with S Luo and X. Ren) Non-hexagonal lattices from a two species interacting system SIAM Journal of Mathematical Analysis 52 (2020), no. 2, 1903–1942.
  98. (with Linfeng Mei) The existence and stability of spike solutions for a chemotaxis system modeling crime pattern formation Math. Models Methods Appl. Sci. 30 (2020), no. 9, 1727–1764.
  99. (with C. Wang, S. Wei and Yifu Zhou) Infinite time blow-up for critical heat equation with drift terms CVPDE 59 (2020), no. 1, Paper No. 3. 35
  100. (with Y. Wu) Local uniqueness of the magnetic Ginzburg-Landau equation Journal of Elliptic and Parabolic Equations 6 (2020), no. 1, 187–209.
  101. (with Y. Wu) Ground states of Nonlinear Schr\"{o}dinger System with Mixed Couplings J. Math Pures Appl. (9) 141 (2020), 50–88.

    102. 2019

  102. (with W. Ao H. Chan, A. Delatorre, M. Fontelos and Mar Gonzalez) On higher dimensional singularities for the fractional Yamabe problem: a non-local Mazzeo-Pacard program Duke Math Journal 168 (2019), no. 17, 3297–3411
  103. (with W. Ao and M. Musso) Nondegeneracy of nonradial sign-changing solutions to the nonlinear Schrodinger equations Bulletin de la SMF 147(1) 2019, 1-49.
  104. (with W. Ao and M. Winter) Stable boundary spike clusters for the two-dimensional Gierer-Meinhardt system J. Math. Pure Appl. 121(2019), 9, 1-46.
  105. (with H. Chan and MASOMEH JAMSHID NEJAD) Lamellar phase solutions for Diblock copolymers with nonlocal diffusions. Physica D: Nonlinear Phenomena 388 (2019), 22–32.
  106. (with Chang, Tzou and Ward) Refined Stability Thresholds for Localized Spot Patterns for the Brusselator Model in $R^2$ European J. Appl. Math. 30 (2019), no. 4, 791–828.
  107. (with Y. Cheng) Fast and slow decaying solutions for $H^1$-supercritical quasilinear Schrodinger equations CVPDE 58 (2019), no. 4, Paper No. 144. 35
  108. (with Juan Davila, Manuel del Pino and Catalina Pesce) Blow-up for the 3-dimensional axially symmetric harmonic map flow into $S^2$ DCDS-A (special volume for L. Caffarelli's 70th birthday) Discrete Contin. Dyn. Syst. 39 (2019), no. 12, 6913–6943.
  109. (with Manuel del Pino and Monica Musso) Type II blow-up in the 5-dimensional energy critical heat equation Acta Math Sinica (Engl Ser.) (special issue to C. Kenig's birthday) 35 (2019), no. 6, 1027–1042.
  110. (with Manuel del Pino, M. Musso, C. Roman) Interior bubbling solutions for the critical Lin-Ni-Takagi problem in dimension 3 Journal d'Analyse Mathematique 137 (2019), no. 2, 813–843.
  111. (with D. Gomez and M.J. Ward) The linear stability of symmetric spike patterns for a bulk-membrane coupled Gierer-Meinhardt model SIAM J. Appl. Dyn. Syst. 18 (2019), no. 2, 729–768.
  112. (with Y. Guo, S. Li and X. Zeng) Ground states of two-component attractive Bose-Einstein condensates I: Existence and Uniqueness Journal of Functional Analysis 276(2019), no.1, 183-230.
  113. (with Y. Guo, S. Li and X. Zeng) Ground states of two-component attractive Bose-Einstein condensates II: Semi-trivial limit behavior Transc. of AMS 371(2019), no. 10, 6903-6948.
  114. (with A. Hyder) Higher order conformally invariant equations in $R^3$ with prescribed volume Comm. Pure Appl. Anal. 18 (2019), no. 5, 2757–2764.
  115. (with A. Hyder) Non-radial solutions to a bi-harmonic equation with negative exponent CVPDE 58 (2019), no. 6, Paper No. 198. 35
  116. (with Y. Liu) On Helmholtz equation and Dancer's type entire solutions for nonlinear elliptic equations Proc. Amer. Math. Soc. 147 (2019), no. 3, 1135–1148
  117. (with Yong Liu) Nondegeneracy, Morse index and orbital stability of the lump solution to the KP-I equation Arch. Mech. Rational Anal. 234 (2019), no. 3, 1335–1389
  118. (with Fanghua Lin) Superfluids passing an obstacle and vortex nucleation DCDS-A (special volume for L. Caffarelli's 70th birthday) Discrete Contin. Dyn. Syst. 39 (2019), no. 12, 6801–6824.
  119. (with M. Musso and S. Deng) Sign-changing blow-up solutions for Yamabe problem International Math. Research Notes (IMRN) 2019, no.13,4159-4197.
  120. (with M. Musso, Y. Sire, Y. Zheng and Yifu Zhou) Infinite time blow-up for the fractional heat equation with critical exponent. Math Annalen 375(2019), no.1-2, 361-424.
  121. (with M. Musso, M. Medina) Desingularization of Clifford Torus and Nonradial Solutions to Yamabe Problem with Maximal Rank Journal of Functional Analysis 276 (2019), no. 8, 2470–2523.
  122. (with Kelei Wang) On Serrin's overdetermined problem and a conjecture of Berestycki, Caffarelli and Nirenberg Comm. PDE 44 (2019), no. 9, 837–858.
  123. (with Kelei Wang) Finite Morse index implies finite ends Comm. Pure Appl. Math. 72(2019),5, 1044-1119
  124. (with Kelei Wang) Second order estimates on transition layers Advances in Mathematics 2019, 106856.
  125. (with Wen Yang) Multi-bump ground states of the fractional Gierer-Meinhardt system on the real line J. Dyn. Diff. Eqns. 31 (2019), no. 1, 385–417.
  126. (with W. Yan and B. Xu) On Lin-Ni's conjecture in dimension four and six Science in China: Mathematics (????:??) 49(2019), No.2, 281–306, doi: 10.1360/N012018-00120

    127. 2018

  127. (with W. Ao and H. Chan) Boundary concentrations on segments for the Lin-Ni-Takagi problem Annali della Scuola Normale Superiore di Pisa 18 (2018), no. 2, 653–696.
  128. (W. Ao, Hardy Chan and Mar Gonzalez) Existence of positive weak solutions for fractional Lane-Emden equations with prescribed singular sets CVPDE 57 (2018), no. 6, 57:149
  129. (with H. Chan) On De Giorgi's Conjecture: recent progress and open problems Science in China: Mathematics 61 (2018), no. 11, 1925–1946.
  130. (with Juan Davila and Manuel del Pino) Nonlocal $s$-minimal surfaces and Lawson cones Journal of Differential Geometry 109(2018), 111-175
  131. (with A. Jevnikar and W. Yang) On the topological degree of the mean field equation with two parameters Indiana Univ. Math. Journal 67(2018), Vol. 1, 29-88.
  132. (with A. Jevnikar and W. Yang) Classification of blow-up limits for the Sinh-Gordon equation Diff. Int. Equations 31 (2018), no. 9-10, 657–684.
  133. (with S. Kim and M. Musso) Existence theorems of the fractional Yamabe problem Analysis & PDE 11(2018), no.1, 75-113.
  134. (with H. Kikuchi) Bifurcation diagram of solutions to elliptic equation with exponential nonlinearity in higher dimensions Proc. Eding. Math. A. 148 (2018), no. 1, 101–122.
  135. (with T. Kolokolnikov, J. Tzou and M. Ward) Stabilizing a homoclinic stripe Philosophical Transactions A of the Royal Society 376 (2018), no. 2135, 20180110, 13 pp.
  136. (with T. Kolokolnikov) Pattern formation in a reaction-diffusion system with space-dependent feed rate SIAM Review 60 (2018), no. 3, 626–645.
  137. (with Yanyan Li and H. Xu) Multi-bump solutions of $-\Delta u =K(x)u^{\frac{n+2}{n-2}}$ on Lattices in ${\mathbb R}^n$ Journal fur die reine und ang. Math. (Crelle's Journal) 2018, no. 743, 163–211.
  138. (with CS Lin and Z. Nie) Toda system and hypergeometric equations Transcations of American Math Society 370 (2018), no. 11, 7605–7626.
  139. (with CS Lin, Y. Lee and W. Yang) Degree counting and shadow system for $SU(3)$ Toda system: one bubbling Journal of Differential Equations 264 (2018), no. 7, 4343–4401.
  140. (with CS Lin, W. Yang and L. Zhang) On rank two Toda system with arbitrary singularities: local max and new estimates Analysis & PDE 11 (2018), no.4, 873-898.
  141. (with Yong Liu) Nondegeneracy of the traveling lump solution to the $2+1$ Toda lattice Journal of Math Physics 59 (2018), no. 10, 101501, 26 pp.
  142. (with Yong Liu and Kelei Wang) On a free boundary problem and minimal surfaces Annals IHP-ANL 35(2018), no. 4, 993-1017.
  143. (with N. T. Fadai and M. Ward) A time-delay in the activator knetics enhances the stability of a spike solution to the Gierer-Meinhardt model DCDS-B 23(2018), no.4, 1431-1458.
  144. (with Justin Tzou and M. Ward) Anomalous Scaling of Hopf Bifurcation Thresholds for the Stability of Localized Spot Patterns for Reaction-Diffusion Systems in 2-D SIAM Journal of Applied Dynamical Systems 17(2018), no. 11, 982-1022.
  145. (with Y. Sire and Y. Zheng) Nondegeneracy of half-harmonic maps from $R$ into $S^1$ Proc. Amer. Math. Soc. 146(2018), no.12, 5263-5268.
  146. (with Lei Zhang) Nondegeneracy of Gauss curvature equation with negative conic singularity Pacific Journal of Mathematics 297(2018), no.2, 455-475.

    147. 2017

  147. (with A. de la Torre, M. del Pino, Mar del mar Gonzalez) Delaunay-type singular solutions for the fractional Yamabe problem Math Annalen 369 (2017), no. 1-2, 597–626.
  148. (with W. Ao and W. Yang) Infinitely many positive solutions of fractional nonlinear Schr$\ddot{\mathrm{O}}$dinger equations with non-symmetric potentials DCDS-A 37 (2017), no. 11, 5561–5601.
  149. (with Hardy Chan) Travelling wave solutions for bistable fractional Allen-Cahn equations with a pyramidal front. Journal of Differential Equations 262 (2017), no. 9, 4567–4609.
  150. (with Juan Davila and L. Dupaigne) On the fractional Lane-Emden equation Trans. Amer. Math. Soc. 369 (2017), no. 9, 6087–6104.
  151. (with M. del Pino and O.Agudelo) Catenoidal layers for the Allen-Cahn equation in bounded domains Chinese Annals of Mathematics (a special volume for Professor H. Brezis' 70th birthday) 38 (2017), no. 1, 13–44.
  152. (with Y. Ding) Multiplicity of semiclassical solutions to nonlinear Schr¨odinger equations J.Fixed Point Theory Appl. (special volume in honor of Professor Paul Rabinowitz's 75th birthday) 19 (2017), no. 1, 987–1010.
  153. (with N. T. Fadai and M.J. Ward) Delayed reaction-kinetics and the stability of spikes in the Gierer-Meinhardt system SIAM Journal Applied Math 77(2017), no.2, 664-696.
  154. (with M. Fazly) On finite Morse index solutions of higher order fractional Lane-Emden equation American Journal of Mathematics 139 (2017), no. 2, 433–460
  155. (with Changfeng Gui and Yong Liu) Two-end solutions to the Allen-Cahn equation in $\mathbb{R}^3$ Advances in Math 320C (2017), 926-992.
  156. (with Yujin Guo and CS Lin) Local uniqueness and refined spike profiles of ground states for two-dimensional attractive Bose-Einstein condensates SIAM J. Math. Anal. 49 (2017), no. 5, 3671–3715
  157. (with ZM Guo and Feng Zhou) Singular radial entire solutions and weak solutions with prescribed singular set for a biharmonic equation J. Diff. Eqns. 263 (2017), no. 2, 1188–1224.
  158. (with S. Kim and M. Musso) A non-compactness result on the fractional Yamabe problem in large dimensions and supplement material Journal of Functional Analysis 273 (2017), no. 12, 3759–3830.
  159. (with Yong Liu and Kelei Wang) Global minimizers of Allen-Cahn equation in dimensions $ n\geq 8$ J.Math Pure Appl. 108 (2017), no. 6, 818–840.
  160. (with S Luo and W. Zou) On a transcendental equation involving quotients of Gamma functions Proc. AMS 145(2017), no. 6, 2623-2637.
  161. (with X. Ren) The spectrum of the torus profile to a geometric variational problem with long range interaction Physica D: Nonlinear Phenomena 351/352 (2017), 62–88.
  162. (with M. Winter) Stable spike clusters for the one-dimensional Gierer-Meinhardt system European Journal of Applied Math 28 (2017), no. 4, 576–635
  163. (with M. Winter and W. Yang) Stable spike clusters for the precurson Gierer-Meinhardt system in $R^2$ CVPDE 56 (2017), no. 5, 56:142

    164. 2016

  164. (with M. del Pino and O.Agudelo) Higher dimensional catenoid, Liouville equation and Allen-Cahn equation Liouville's equation International Math. Research Note (IMRN) 2016, no. 23, 7051–7102
  165. (with WW Ao and CS Lin) On Non-topological Solutions of the $A_2$ and $B_2$ Chern-Simons System (112 pages) Memoirs of American Mathematical Society 239(2016), no. 1132.
  166. (with WW Ao and CS Lin) On non-topological solutions of the $G_2$ Chern-Simons system Communications Analysis and Geometry 24 (2016), no. 4, 717–752.
  167. (with WW Ao, M. Musso and F. Pacard) Solutions without any symmetry for semilinear elliptic problems Journal of Functional Analysis 270(2016), no.3, 884-956.
  168. (with W. Ao and W. Yao) Uniqueness and nondegeneracy of sign-changing radial solutions of an almost critical problem Advances in Differential Equations 21(2016), no.11-12, 1049-1084.
  169. (with Juan Davila and Kelei Wang) Qualitative Analysis of Rupture Solutions for an MEMS Problem Ann.Inst. Henri.Poincare NonLinearie 33(2016), no.1, 221-242
  170. (with Z.Du) Clustering layers for the Fife-Greenlee problem in $\mathbb{R}^n$ Proc. Royal Soc. Edin. Math Section A 146(2016), no. 1, 107-139.
  171. (with Z. Du, C. Gui and Y. Sire) Layered solutions for a fractional inhomogeneous Allen-Cahn equation NoDEA 23(2016), no.3, 23:29
  172. (with Changfeng Gui and Yong Liu) On variational characterization of four-end solutions of the Allen-Cahn equation in the plane Journal of Functional Analysis 271(2016), no. 10, 2673-2700.
  173. (with ZM Guo and Wen Yang) On non-radial singular solutions of supercritical bi-harmonic equations Pacific Journal of Math. 284(2016), no.2, 395-430.
  174. (with M. Fazly) On stable solutions of the fractional Henon-Lane-Emden equation Comm. Contemp. Math. 18(2016), No. 5, 1650005 (24pages)
  175. (with Meiyue Jiang and Liping Wang) $2\pi$-periodic self-similar solutions for the anisotropic affine curve shortening problem II DCDS-A 36(2016), no.2, 785-803.
  176. (with CS Lin and L. Zhang) Local profile of fully bubbling solutions to SU(n+1) Toda Systems Journal of Europ.Math. Soc. (JEMS) 18(2016), no. 8, 1707-1728.
  177. (with Bruno Premoselli) Non-compactness and infinite number of conformal initial data sets in high dimensions Journal of Functional Analysis 270(2016), no.2, 718-747.
  178. (with M. Musso) Sign-changing blowing-up solutions for supercritical Bahri-Corn's problem CVPDE 55(2016), no.1, 55:1
  179. (with A. Pistoia and M. Musso) New blow-up phenomena for {\em SU(n+1)} Toda system JDE 260(2016), no. 7, 6232-6266.
  180. (with M. Musso and S. Yan) Infinitely many positive solutions for an nonlinear field equation with super-critical growth Proceedings of London Math Society 112(2016), no.1, 1-26.
  181. (with S. Santra) Positive solutions of nonlinear Schrodinger equation with peaks on a Clifford torus Mathematische Nachrichten 289(2016), no. 8-9, 1131-1147.
  182. (with Santra) On a singular perturbed problem in an annulus Annali della Scuola Normale Superiore di Pisa, Classe di Scienze (5)15(2016), 837-857
  183. (with Kelei Wang) On the uniqueness of solutions of an nonlocal elliptic system Math. Annalen 365(2016), no.1-2, 105-153.
  184. (with Jun Yang) Traveling vortex helicies for Schr\"odinger Map Equation Transc. of Amer. Math. Soc. 368(2016), no.4, 2589-2622.

    185. 2015

  185. (with WW Ao and CS Lin) On Toda system with Cartan matrix $G_2$ Proc. Amer. Math. Soc. 143(2015), no.8, 3525-3536.
  186. (with M. del Pino and O. Agudelo) Multiple Catenoidal End Solutions to the Allen-Cahn Equation in $\R^3$ J. Math. Pures Appl. 103(2015), no.1, 142-218
  187. (with M. del Pino and F. Pacard) Serrin's overdetermined problems and constant mean curvature surfaces Duke Math Journal 164(2015), no.14, 2643-2722.
  188. (with M. del Pino and Wei Yao) Intermediate Reduction Methods and Infinitely many positive solutions of nonlinear Schr\"{o}dinger equations with non-symmetric potentials Cal.Var. PDE 53(2015), no.1-2, 473-523.
  189. (with M. Fazly and X. Xu) A point-wise inequality for the fourth order Lane-Emden equation Analysis & PDE 8(2015), no. 7, 1541-1563.
  190. (with M. Grossi and F. Gladiali) On a general $SU(3)$ Toda system CVPDE 54(2015), no.4, 3353-3372.
  191. (with D. Iron, J. Rumsey, M.J. Ward) On accurately estimating stability threshold for periodic spot patterns of reaction-diffusion systems in $R^2$ European Journal of Applied Math 26(2015), no.3, 325-353.
  192. (with M. Kowalczyk and Yong Liu) Singly periodic solutions of the Allen-Cahn equation and the Toda lattice Comm. Part. Diff. Eqns. 40(2015), no.2, 329-356.
  193. (with M. Kowalczyk, Yong Liu and Frank Pacard) End-to-end construction for the Allen-Cahn equation in the plane Cal. Var. PDE 52(2015), no.2, 329-356.
  194. (with CS Lin and L. Zhang) Classification of blowup limits for $SU(3)$ singular Toda systems Analysis and PDE 8(2015), no. 4, 807-837.
  195. (with CS Lin and L. Zhang) Convergence rate, location and $\partial_z^2$ condition for fully bubbling solutions to $SU(n+1)$ Toda systems Advances in Mathematics 285(2015), 1189-1224.
  196. (with M. Musso) Nondegeneracy of nonradial nodal solutions to Yamabe problem Comm. Math. Physics 340(2015), no.3, 1049-1107
  197. (with Xiaofeng Ren) A double bubble assembly as a new phase of a ternary inhibitory system Arch Rat Mech Anal 215(2015), no.3, 967-1034.
  198. (with Y. Sire) On a fractional Henon equation and applications Math Research Letters 22(2015), no. 6, 1791-1804.
  199. (with Kelei Wang) Analysis of Blow-up Locus and Existence of Weak Solutions for Nonlinear Supercritical Problems Int. Math. Res. Not. IMRN 2015, no.10, 2634-2670
  200. (with M. Winter) Existence and stability of a spike in the central component for a consumer chain model Journal of Dynamical and Differential Equations 27(2015), no.3-4, 1141-1171.
  201. (with S. Yan) Clustered bubbles for An Elliptic problem with critical growth Nonlinear Analysis:TMA 119(2015), 46-61.

    202. 2014

  202. (with WW Ao) Infinitely many positive solutions for nonlinear equations with non-symmetric potential Cal Var. PDE 51(2014), no.3-4, 761-798.
  203. (with H. Berestycki and M. Winter) Existence of Symmetric and Asymmetric Spikes for a Crime Hotspot Model SIAM J. Math. Analysis 46(2014), no.1, 691-719
  204. (with Juan Davila, Louis Dupaigne and Kelei Wang) A Monotonicity Formula and a Liouville-type Theorem for a Fourth Order Supercritical Problem Advances in Mathematics 258(2014), 240-285
  205. (with Juan Davila and Manuel del Pino) Concentrating standing waves for the fractional nonlinear Schrodinger equation J. Diff. Eqns. 256(2014), no.2, 858-892.
  206. (with Daomin Cao and Z. Liu) Regularization of point vortices pairs for the Euler equation in dimension two Archive Rat. Mech. Anal. 212(2014), no.1, 179-217
  207. (with Y.Guo and B. Li) Entire nonradial solutions for non-cooperative coupled elliptic system with critical exponents J. Diff. Eqns. 256(2014), no. 10, 3463-3495
  208. (with ZM Guo) Liouville Type Results and Regularity of the Extremal Solutions of Biharmonic equation with negative exponents DCDS-A 34(2014), no.6, 2561-2580.
  209. (with ZM Guo) Rupture solutions of an elliptic equation with a singular nonlinearity Proc. Roy. Soc. Edin., A 144(2014), no. 5, 905-924.
  210. (with D. Iron, J. Rumsey and M. Ward ) Logarithmic Expansions and the Stability of Periodic Patterns of Localized Spots for Reaction-Diffusion Systems in $R^2$ Journal of Nonlinear Science 24(2014), no. 5, 857-912.
  211. (with T. Kolokolnikov and A. Alcolado) Basic mechanisms driving complex spike dynamics in a chemotaxis model with logistic growth. SIAM Journal of Applied Mathematics 74(2014), no.5, 1375-1396.
  212. (with T. Kolokolnikov and M.J. Ward) The stability of steady-state hotspot patterns for a reaction-diffusion model of urban crime DCDS-B 19(2014), no.5, 1373-1410.
  213. (with Xiaofeng Ren) Double tori solution to an equation of mean curvature and Newtonian potential Cal Var PDE 49(2014), no.3-4, 987-1018
  214. (with Xiaofeng Ren) Asymmetric and symmetric double bubbles in an inhibitory ternary system SIAM J. Math. Anal. 46(2014), no.4, 2798-2852.
  215. ( with S. Santra) Profile of the least energy solution of a singular perturbed Neumann problem with mixed powers Annali di Matematica Pura ed Applicata (4) 193(2014), no.1, 39-70.
  216. (with M. Winter) Stability of cluster solutions to a tritrophic food chain model Journal of Mathematical Biology 68(2014), no.1-2, 1-39.

    217. 2013

  217. (with WW Ao and Jing Zeng) An optimal bound on the number of interior spike solutions for the Lin-Ni-Takagi problem Journal of Functional Analysis 265 (2013), no. 7, 1324–1356.
  218. (with H. Berestycki, TCLin and CY Zhao) On Phase-Separation Model: Asymptotics and Qualitative Properties Archive Rational Mechanics Analysis 208(2013), no.1, 163-200.
  219. (with H. Berestycki, S. Terracini and K. Wang) On Entire Solutions of an Elliptic System Modeling Phase Separations Advances in Mathematics 243(2013), pp. 102 - 126
  220. (with M. del Pino and M. Kowalczyk) Traveling waves with multiple and non-convex fronts for a bistable semilinear parabolic equation Comm. Pure Appl. Math. 66(2013), no.4, 481-547.
  221. (with M. del Pino and M. Kowalczyk) Entire Solutions of the Allen-Cahn Equation and Complete Embedded Minimal Surfaces of Finite Total Curvature Journal of Differential Geometry 83(2013), no.1, 67-131.
  222. (with Yanheng Ding and T. Xu) Existence and concentration of semi-classical solutions for an nonlinear Maxwell-Dirac system Journal of Mathematical Physics 54(2013), no.6, 061505, 33pp.
  223. (with Yuxia Guo and B. Li) Large energy entire solutions for the Yamabe type problem of polyharmonic operator J. Diff. Eqns. 254(2013), no.1, 199-228
  224. (with E. Hebey) Schrodinger-Poisson system in the 3-sphere Cal Var PDE 47(2013), no.1-2, 25-54.
  225. (with Fouad Hadj Selem and Hiroaki Kikuchi) Existence and uniqueness of singular solution to stationary Schr\"{o}dinger equation with supercritical nonlinearity DCDS-A 33 (2013), no. 10, 4613–4626.
  226. (with T. Kolokolnikov and W. Yang) On large ring solutions for Gierer-Meinhardt system in $R^3$ Journal of Differential Equations 255(2013), no.7, 1408-1436.
  227. (with TC Lin and Jun Yang) Vortex rings for the Gross-Pitaevskii equation in $\R^3$ J. Math. Pures Appl. (9) 100(2013), no.1, 69-112.
  228. (with L.Ma) Stability and multiple solutions to Einstein-scalar field Lichnerowicz equation on manifolds J. Math. Pures App. (9)99(2013), no.2, 174-186.
  229. (with Frank Pacard) Stable solutions of the Allen-Cahn equation in dimension $8$ and minimal cones Journal of Functional Analysis 264(2013), no.5, 1131-1167.
  230. (with Xiaofeng Ren) A double bubble in a ternary system with long range interaction. Archive Rational Mech. Analysis 208(2013), no.1, 201-253.
  231. (with S. Santra) New entire positive solution for the nonlinear Schr\"{o}dinger equation: Coexistence of fronts and bumps American Journal of Mathematics 135(2013), no.2, 443-491.
  232. (with F. Ting) Multi-vortex non-radial solutions to the magnetic Ginzburg-Landau equations Comm. Math. Phys. Volume 317, Issue 1 (2013), Page 69-97
  233. (with L. Wang) Infinite Multiplicity for an Inhomogeneous Supercritical Problem in Entire Space Comm. Pure Appl. Anal. 12(2013), No. 3, 1243-1257.
  234. (with Kelei Wang) On solutions with polynomial growth to an autonomous nonlinear elliptic problem Advance Nonlinear Studies 13(2013), no.4, 921-932.
  235. (with Xingwang Xu and Wen Yang) On the classification of stable solution to biharmonic problems in large dimensions Pacific Journal of Mathematics 263(2013), no.2, 495-512.
  236. (with S. Yan ) Infinitely many non-radial solutions for the H\'enon equation with critical growth Revista Matematica Iberoamericana 29(2013), no.3, 997-1020
  237. (with Dong Ye) Liouville Theorems for finite Morse index solutions of Biharmonic problem Mathematische Annalen 356(2013), no.4, 1599-1612.
  238. (with C.Zhao) Non-compactness of the Prescribing $Q-$curvature problem in large dimensions Cal. Var. PDE 46(2013), No.1, 123-164

    239. 2012

  239. (with A. Aftalion and P. Mason) Vortex-peak interaction and lattice shape in rotating two-component Bose-Einstein condensates. Physical Review A 85(2012), no.3, 033614.
  240. (with Wenyi Chen and S. Yan) Infinitely many solutions for the Schr\"odinger equations in $\R^N$ with critical growth Journal of Differential Equations 252(2012), no.3, 2425-2447.
  241. (with J. Davila) Point ruptures for a MEMS equation with fringing field Comm. Part. Diff. Eqns. 37(2012), 1462-1493.
  242. (with EN Dancer and ZM Guo) Non-radial singular solutions of Lane-Emden equation in $R^N$ Indiana Univ. Math. Journal 61(2012), no.5, 1971-1996.
  243. (with Manuel del Pino and Mike Kowalczyk) On De Giorgi's conjecture and beyond Proceedings of National Acad. of Sciences (PNAS) 109(2012), vol. 18, 6845-6850.
  244. (with E. Hebey) Resonant states for the static Klein-Gordon-Maxwell-Proca system Math Research Letters 19(2012), no.4, 953-967.
  245. (with Chang-Shou Lin and Dong Ye) Classification and nondegeneracy of $SU(n+1)$ Toda system with singular sources Inventiones Mathematicae 190(2012), no.1, 169-207.
  246. (with Chang-Shou Lin and Chunyi Zhao) Sharp estimates for fully bubbling solutions of a SU(3) Toda system Geom. Funct. Anal. 22(2012), no.6, 1591-1635.
  247. (with CSLin and CY Zhao) Asymptotic behavior of $SU(3)$ Toda system in a bounded domain Manuscripta Math. 137(2012), no.1-2, 1-18.
  248. (with Monica Musso) Nonradial solutions to critical elliptic equations of Caffarelli-Kohn-Nirenberg type International Mathematics Research Notices. 18(2012), 4120-4162.
  249. (with Frank Pacard and M. Musso) Finite-energy sign-changing solutions with dihedral symmetry for the stationary non linear Schr\"{o}dinger equation Journal of European Mathematical Society 14(2012), no.6, 1923-1953.
  250. (with A. Pakylak and F. Ting) Multi-vortex solutions to Ginzburg-Landau equations with external potential Archive Rational Mech. Analysis 204(2012), no.1, 314-354.
  251. (with M. Winter) Flow-Distributed Spikes for Schnakenberg Kinetics Journal of Mathematical Biology 64(2012), no.1-2, 211-254.
  252. (with Jun Yang) Vortex rings pinning for the Gross-Pitaevskii equation in three dimensional space SIAM Journal of Mathematical Analysis 44(2012), no.6, 3991-4047.
  253. (with W. Yao) Uniqueness of positive solutions to some coupled nonlinear Schr\"{o}dinger equations CPAA 11(2012), no.3, 1003-1011

    254. 2011

  254. (with Weiwei Ao and M. Musso) On Spikes Concentrating on Line-Segments to a Semilinear Neumann Problem Journal of Differential Equations 251(2011), no.4-5, 881-901.
  255. (with Weiwei Ao and M. Musso) Triple Junction Solutions for a Singularly Perturbed Neumann Problem SIAM Journal of Mathematical Analysis 43(2011), no.6, 2519-2541.
  256. (with D. Cao and I. Chern) On ground states of spinor Bose-Einstein condensates NoDEA 18(2011), no.4, 427-445.
  257. (with E.Dancer and S. Santra) Least energy nodal solution of a singular perturbed problem with jumping nonlinearity Annali della Scuola Normale Superiore di Pisa, Classe di Scienze. (5) 10(2011), no.1, 19-36.
  258. (with O. Druet and F. Robert) The Lin-Ni's problem for mean convex domains Memoirs of American Mathematical Society November 30, 2011
  259. (with Manuel del Pino) Solutions to the Allen-Cahn Equation and Minimal Surfaces Milan Journal of Mathematics 79(2011), 39-65.
  260. (with M. del Pino and M. Kowalczyk) On De Giorgi Conjecture in Dimensions $N \geq 9$ (final version) Annals of Mathematics 174 (2011), no.3, 1485-1569.
  261. (with Yuxin Ge and Feng Zhou) A critical elliptic problem for polyharmonic operators J. Funct. Analysis 260(2011), no.8, 2247-2282.
  262. (with ZM Guo) Global solution branch and Morse index estimates of a semilinear elliptic equation with super-critical exponent Trans. American Math. Soc. 363(2011), no.9, 4777-4799
  263. (with Z. Guo, Z. Liu F. Zhou) Bifurcations of some elliptic problems with a singular nonlinearity via Morse index CPAA 10(2011), no.2, 507-525.
  264. (with Meiyue Jiang and LP Wang) $2\pi$-periodic self-similar solutions for the anisotropic affine curve shortening problem Cal. Var. PDE 41(2011), no.3-4, 535-565.
  265. (with Theodore Kolokolnikov) Stability of spiky solutions in a competition model with cross-diffusion SIAM Journal of Applied Mathematics 71(2011), no.4, 1428-1457.
  266. (with CS Lin and LP Wang) Topological Degree For Solutions of A Fourth Order Mean Field Equation Math. Zeit 268(2011), 675-705.
  267. (with X.Ren) A toroidal tube solution of a nonlocal geometric problem Interfaces and Free Boundaries 13 (2011), no. 1, 127–154.
  268. (with S. Santra) Asymptotic behavior of solutions of a biharmonic Dirichlet problem with large exponents Journal d'Analyse Math. 115(2011), 1-31.
  269. (with L. Wang and S. Yan) On Lin-Ni's Conjecture in Convex Domains Proc. London Math. Soc. 102(2011), 1099-1126.
  270. (with L. Wang and J. Yang) On Ambrosetti-Malchiodi-Ni Conjecture for General Hypersurfaces Communications in Part. Diff. Eqns. 36(2011), vol. 12, 2117-2161
  271. (with L. Wei and F. Zhou) Mixed interior and boundary nodal bubbling solutions for a sinh-Poisson equation Pacific Journal of Mathematics 250(2011), no.1, 225-256.
  272. (with W. Yao) Asymptotic axisymmetry of the subsonic traveling waves to the Gross-Pitaevskii equation Comm. Contemp. Math. 13(2011), no.6, 1095-1104.
  273. (with S. Yan) Infinitely many positive solutions for an elliptic problem with critical or super-critical growth J. Math Pures Appl. (9) 96(2011), no.4, 307-333.
  274. (with CY Zhao and F. Zhou) On nondegeneracy of solutions of $SU(3)$ Toda system CRAS 349(2011), no.3-4, 185-190.
  275. (with EN Dancer and S. Santra) Asymptotic behavior of the least energy solution of a problem with competing powers Journal of Functional Analysis 261(2011), 675-705.

    276. 2010

  276. (with H. Berestycki) On Least Energy Solutions to A Semilinear Elliptic Equation in A Strip DCDS-A 28(2010), no.3, 1083-1099
  277. (with EN Dancer and T. Weth) A priori bounds versus multiple existence of positive solutions for a nonlinear Schrodinger system AIHP 27 (2010), pp. 953-969
  278. (with Manuel del Pino and M. Kowalczyk) The Jacobi-Toda system and foliated interfaces DCDS-A 28(2010), no.3, 975-1006.
  279. (with M. del Pino, M. Kowalczyk and F. Pacard) The Toda system and multiple-end solutions of autonomous planar elliptic problems Advances in Mathematics 224(2010), no.4, 1462-1516.
  280. (with M. del Pino, M. Kowalczyk and F. Pacard) Multiple-end solutions to the Allen-Cahn equations in $R^2$ Journal of Functional Analaysis 258(2010), no.2, 458-503.
  281. (with Manuel del Pino, M. Kowalczyk and Jun Yang) Interface foliation near minimal submanifolds in Riemannian manifolds with positive Ricci curvature Geom. Funct. Anal. 20(2010), no.4, 918-957.
  282. (with Qiang Du and C. Zhao) Vortex Solutions of the High-$\kappa$ High-field Ginzburg-Landau Model with an Applied Current SIAM J. Math. Anal. 42(2010), no.6, 2368-2401.
  283. (with ZM Guo) Qualitative properties of entire radial solutions for a biharmonic equation with supcritical nonlinearity Proc. American Math. Soc. 138(2010), no.11, 3957-3964.
  284. (with FH Lin) Traveling Wave Solutions of Schr\"odinger Map Equation Comm. Pure Appl. Math. 63(2010), no.12, 1585-1621.
  285. (with TC Lin and Xiaojin Chen) Blow up and solitary waves with ring profiles for two-component nonlinear Schrodinger equations Phys. D: Nonlinear Phenomena 239(2010), no.10, 613-626.
  286. (with T-C Lin and W. Yao) Orbital stability of bound states of nonlinear Schr\"{o}dinger equations with linear and nonlinear lattices J. Diff. Eqns. 249(2010), no.9, 2111-2146.
  287. (with H. Tse and M. Winter) The Gierer-Meinhardt System on a Compact Two-Dimensional Riemannian Manifold: Interaction of Gaussian Curvature and Green's Function J. Math. Pures Appl. 94(2010), no.4, 366-397.
  288. (with Liping Wang and Shusen Yan) A Neumann Problem with Critical Exponent in Non-convex Domains and Lin-Ni's Conjecture Transcation of Amer. Math. Soc. 362(2010), no.9, 4581-4615.
  289. (with M. Winter) Stability of Spiky Solutions in a Reaction-Diffusion System with Four Morphogens on the Real Line SIAM J. Math. Anal. 42(2010), no.6, 2818-2841.
  290. (with S. Yan) On an elliptic problem with critical growth and a stronger Lazer-McKenna conjecture Ann. Scuola. Norm. Pisa (5)9(2010), no.2, 423-457.
  291. (with S. Yan) Infinitely many positive solutions for the nonlinear Schr\"odinger equations in $ R^N$ Cal.Var. PDE 37(2010), 423-439.
  292. (with Shusen Yan) Infinitely many solutions for the prescribed scalar curvature problem on $\Sn^N$ Journal Functional Analysis 258(2010), 3048-3081.
  293. (with Jun Yang) Toda system and cluster phase transition layers in an inhomogeneous phase transition model Asymptotic Analysis 69(2010), no.3-4, 175-218.
  294. (with Dong Ye) On MEMS equations with fringing fields Proc. American Math. Soc. 138(2010), no.5, 1693-1699.

    295. 2009

  295. (with E.N. Dancer) Spike Solutions in coupled nonlinear Schr\"odinger equations with Attractive Interaction Transc. American Math. Soc. 361(2009), no.3, 1189-1208.
  296. (with P. Esposito) Non-simple Blow-up Solutions for the Neumann two-dimensional $\sinh-$Gordon equation Cal Var. PDE 34(2009), no.3, 341-375.
  297. (with YX Guo) Supercritical biharmonic elliptic problems in domains with small holes Math. Nach. 282(2009), no.12, 1724-1739.
  298. (with D. Iron, T. Kolokolonikov, J. Rumsey ) Stability of curved interfaces in the perturbed two-dimensional Allen-Cahn system SIAM Journal of Applied Math. 69(2009), no.5, 1228-1243.
  299. (with Theodore Kolokolnikov and M. Ward) Spot self-replication and dynamics for the Schnakenburg model in a two-dimensional domain Journal of Nonlinear Science 19(2009), no.1, 1-56.
  300. (with T. Kolokolnikov and M. Winter) Existence and Stability Analysis of Spiky Solutions for the Gierer-Meinhardt System with Large Reaction Rates Physica D: Nonlinear Phenomena 238(2009), no.16, 1695-1710.
  301. (with Fanghua Lin and Taichia Lin) Skymions in Gross-Pitaevskii Functionals Acta Mathematica Scientia 2009, 29B(3): 751-776. Special Volume dedicated to Prof. Wu Wenjun's 90th birthday.
  302. (with PK Maini and M. Winter) Stability of Spikes in the Shadow Gierer-Meinhardt system with Robin Boundary Conditions Chaos (special issue on pattern formations in reaction-diffusion systems) 17(2009),037106, 16pp. .
  303. (with X.Ren) On a phase field problem driven by interface tension and interface curvature Eur.J. Appl.Math. 20(2009), no.6, 531-556.
  304. (with X. Ren) Oval shaped droplet solutions in the saturation process of some pattern formation problems SIAM Journal of Applied Mathematics 70(2009), no.4, 1120-1138.
  305. (with S.Santra) Homoclinic solutions for fourth order travelling wave equations SIAM J. Math. Anal. 41(2009), no.5, 2038-2056.
  306. (with M. Winter) Spikes for the Gierer-Meinhardt system with discontinuous diffusion coefficients Journal of Nonlinear Science 19(2009), no.3, 301-339.
  307. (with M. Winter) Strongly Interacting Bumps for the Schrodinger-Newton Equations Journal of Mathematical Physics 50(2009), no.1, 012905.
  308. (with M. Winter) On the Gierer-Meinhardt system with precursors DCDS-A, special issue for Prof. Mimura's 65th Birthday 25(2009), no.1, 363-398.
  309. (with Xingwang Xu) Prescribing $Q-$curvature problem on $S^n$ Journal of Functional Analaysis 257(2009), no.7, 1995-2023.
  310. (with J. Yang) Solutions with transition layer and spike in an inhomogeneous phase transition model Journal of Differential Equations 246(2009), no.9, 3642-3667.

    311. 2008

  311. (with C. Bandle) Multiple Clustered Layer Solutions for Semilinear Elliptic Problems on $S^n$ Comm. Partial Diff. Equations 33(2008), no.4-6, 613-635.
  312. (with Juan D\'avila, Manuel del Pino and Monica Musso) Fast and slow decay solutions for supercritical elliptic problems in exterior domains Calculus of Variations and PDE 32(2008), no.4, 765-786.
  313. (with Manuel del Pino and Mike Kowalczyk ) The Toda system and clustering interfaces in the Allen-Cahn equation Archive Rational Mechanical Analysis 190(2008), no.1, 141-187.
  314. (with M. del Pino and M. Kowalczyk) On De Giorgi Conjecture in Large Dimensions C. R. A. S. 346(2008), no.23-24, 1261-1266.
  315. (with Y. Ding) Stationary states of nonlinear Dirac equations with general potentials Reviews in Mathemmatical Physics 20(2008), no.8, 1007-1032.
  316. (with ZM Guo) Asymptotic Behavior of touch-down solutions and global bifurcations for an elliptic problem with a singular nonlinearity Comm. Pure Appl. Anal. 7(2008), no.4, 765-786.
  317. (with ZM Guo) Infinitely many turning points for an elliptic problem with a singular nonlinearity Journal of London Mathematical Society, 78(2008), no.1, 21-35.
  318. (with Z.M. Guo) Entire solutions and global bifurcations for a biharmonic equation with singular nonlinearity in $\mathbb R^3$ Adv. Diff. Eqns. 13(2008), no.7-8, 743-780.
  319. (with ZM Guo) On a fourth order elliptic problem with negative exponent SIAM J. Math. Anal. 40(2008/09), no.5, 2034-2054.
  320. (with ZM Guo) On solutions with point ruptures for a semilinear Elliptic problem with singularity Methods of Analysis and Applications, special issue on MEMS 15(2008), no.3, 377-390.
  321. (with YX Guo) Nonexistence of positive finite Morse index solutions to an elliptic problem with singular nonlinearity Methods of Analysis and Applications, special issue on MEMS 15(2008), no.3, 377-390.
  322. (with Theodore Kolokolnikov) Positive Clustered Layered Solutions For the Gierer-Meinhardt System Journal of Differential Equations 245(2008), no.4, 964-993.
  323. (with TC Lin) Orbital stability of bound states of semi-classical nonlinear Schr\"{o}dinger equations with critical nonlinearity SIAM J. Mathematical Analysis 40(2008), no.1, 365-381.
  324. (with Li Ma) Properties of positive solutions to an Elliptic Equation with negative exponent Journal of Functional Analysis 254(2008), no.4, 1058-1087.
  325. (with F.Mahmoudi and A. Malchiodi) Transition Layer for the Heterogeneous Allen-Cahn Equation Ann. Non linearie, Annoles de l'Institut H. Poincare, 25(2008), no.3, 609-631.
  326. (with X. Ren) The critical mass constraint in the Cahn-Hilliard equation Interfaces and Free Boundary Problems 10(2008), no.3, 301-338.
  327. (with X. Ren) Spherical solutions to a free boundary problem from diblock copolymer morphology SIAM Journal of Mathematical Analysis 39(2008), no.5, 1497-1535.
  328. (with F. Robert) Asymptotic behavior of a fourth order equation with Dirichlet boundary condition Indiana Univ. Math. J. 57(2008), no.5, 2039-2060.
  329. (with Wang Hung Tse and M. Winter) Spikes for the Gierer-Meinhardt System with Many Segments of Different Diffusivities Bulletin of Academia Sinica (New Series), Special volume in celebration of Prof. M. Mimura's 65th birthday 3(2008), no.4, 525-566.
  330. (with Liping Wang) Solutions with Interior Bubble and Boundary Layer for an Elliptic Problem DCDS-A (special volume in celebration of Dancer's sixtieth birthday) 21(2008), no.1, 333-351.
  331. (with Tobias Weth ) Radial solutions and phase separation in a system of two coupled Schr\"odinger equations, Archive Rational Mechanical Analysis 190(2008), no.1, 83-106.
  332. (with T. Weth) Asymptotic behavior of solutions of planar elliptic systems with strong competition Nonlinearity 21(2008), no.2, 305-317.
  333. (with M. Winter) Stationary Multiple Spots for Reaction-Diffusion Systems Journal of Mathematical Biology 57(2008), no.1, 53-89.
  334. (with M. Winter) Mutually Exclusive Spiky Pattern and Segmentation Modeled by the Five-Component Meinhardt-Gierer System SIAM J. Appl. Math. 69(2008), no.2, 419-452.
  335. (with Jun Yang) Toda system and interior clustering line concentration for a singularly perturbed Neumann problem in two dimensional domain DCDS-A 22(2008), no.3, 465-508.
  336. (with Dong Ye) Nonradial solutions for a conformally invariant fourth order equation in $R^4$ Cal. Var. PDE 32(2008), no.3, 373-386.
  337. (with F. Zhou and Dong Ye) Analysis of boundary bubbling solutions for an anisotropic Emden -Fowler equation, Ann. Non linearie, Annoles de l'Institut H. Poincare, 25(2008), no.3, 425-447.

    338. 2007

  338. (with C. Bandle) Nonradial Clustered Spike Solutions for Semilinear Elliptic Problems on $S^n$ J' Analyse Math. 102(2007), 181-208.
  339. (with T. Bartsch and Zhi-qiang Wang) Bound states for a coupled nonlinear Schrodinger system JFPTA 2(2007), no.2, 353-367.
  340. (with E.Dancer) Sign-changing solutions for supercritical elliptic problems in domains with small holes Manuscripta Mathematica 123(2007), no.4, 493-511.
  341. (with D'Aprile) Clustered Solutions Around Harmonic Centers to a Coupled Elliptic System . Ann. Non linearie, Annoles de l'Institut H. Poincare, 24(2007), no.4, 605-628
  342. (with Juan D\'avila, Manuel del Pino and M. Musso) Standing waves for supercritical nonlinear Schr\"odinger equations . Journal of Differential Equations 236(2007), no.1, 164-198.
  343. (with M. del Pino and M. Kowalczyk) Concentration on curves for nonlinear Schr\"odinger equations Communications on Pure and Applied Mathematics 60 (2007), no. 1, 113-146.
  344. (with M. del Pino) Supercritical elliptic problems in domains with small holes . Ann. Non linearie, Annoles de l'Institut H. Poincare, 24(2007), no.4, 507-520.
  345. (with YH Ding) Semiclassical states for nonlinear Schrodinger equations with sign-changing potentials Journal of Functional Analysis 251(2007), no.2, 546-572.
  346. (with Th. Kolokolnikov and Michael Ward ) Self-replication of mesa patterns in reaction-diffusion systems, Physica D: Nonlinear Phenomena 236(2007), no.2, 104-122.
  347. (with Z. Guo) Symmetry of Nonnegative Solutions of a Semilinear Elliptic Equation with Singular Nonlinearity . Proc. Royal. Soc. Edinburgh. Section A. (Mathematics) 137(2007), no.5, 963-994.
  348. (with Guo ZM) On the Cauchy problem for a reaction-diffusion equation with a singular nonlinearity J. Diff. Eqns. 240(2007), 181-208.
  349. (with F.-H. Lin and W.-M. Ni) On the Number of Interior Peak Solutions for A Singularly Perturbed Neumann Problem Communications on Pure and Applied Mathematics 60 (2007), no. 2, 252-281.
  350. (with C.-S. Lin) Uniqueness of multiple-spike solutions via the Method of Moving Planes Pure and Applied Mathematics, A Quarterly Journal (special volume in honour of L. Simon's 60th birthday), 3(2007), no.2, part 2, 689-735.
  351. (with CS Lin) Sharp Estimates For Bubbling Solutions of A Fourth Order Mean Field Equation Annali della Scuola Normale Superiore di Pisa, Classe di Scienze, (5)6(2007), no.4, 599-630.
  352. (with CS Lin and L. Wang) Bubble Accumulations In An Elliptic Neumann Problem With Critical Sobolev Exponent . Cal. Var. PDE 30(2007),no.2, 153-182.
  353. (with TCLin) Half-Skyrmions and Spike-Vortex Solutions of Two-component Nonlinear Schr\"{o}dinger Systems . Journal of Mathematical Physics 48(2007), no.5, 053518.
  354. (with A. Malchiodi) Boundary Interface for the Allen-Cahn Equation Journal of Fixed Point Theory and Applications (JFPTA) 1(2007), no.2, 305-336.
  355. (with A. Malchiodi and W.-M. Ni) Boundary Clustered Interfaces for Allen Cahn Equation . Pacific Journal of Mathematics , 229(2007), no.2, 447-468.
  356. (with J. Norbury and M. Winter) Stability of patterns with arbitrary period for a Ginzburg-Landau equation with a mean field . European Journal of Applied Mathematics 18(2007), no.2, 129-151.
  357. (with Xiaofeng Ren) Single droplet pattern in the cylindrical phase of diblock copolymer morphology Journal of Nonlinear Science 17(2007), no.5, 471-503
  358. (with X. Ren) Many droplet pattern in the cylindrical phase of diblock copolymer morphology Reviews in Mathematical Physics 19(2007), no.8, 879-921.
  359. (with M. Winter) Symmetric and asymmetric clusters in an elliptic system. NoDEA, 14(2007), no.5-6, 787-823.
  360. (with M. Winter) Existence, Classification and Stability Analysis of Multiple-peaked Solutions for the Gierer-Meinhardt System in $R^1$ Methods Appl. Anal. 14(2007), no.2, 119-163.
  361. (with Tobias Weth ) Nonradial Symmetric Bound States for a System of Coupled Schr\"odinger Equations Rendiconti Lincei:Matematica e Applicazioni 18(2007), no.3, 279-293.
  362. (with S. Yan) Arbitrary many boundary peak solutions for An Elliptic Neumann problem with critical growth J. Math. Pures Appl. (9)88(2007), no.4, 350-378.
  363. (with S. Yan) Lazer-Mckenna conjecture: the critical case . Journal of Functional Analysis 244(2007), 639-667.
  364. (with S. Yan) New Solutions For Nonlinear Schr\"odinger Equations with critical nonlinearity . Journal of Differential Equations 237(2007), no.2, 446-472.
  365. (with Jun Yang) Concentration on Lines for a Singularly Perturbed Neumann Problem in Two-Dimensional Domains , Indiana Univ. Math. Journal, 56(2007), no.6, 3025-3073.
  366. (with D. Ye and F. Zhou) Bubbling Solutions for an Anisotropic Emden-Fowler Equation Cal. Var. and Part. Diff. Eqns. 28(2007), 217-247.

    367. 2006

  367. (with T. D'Aprile) Standing waves in the Maxwell-Schrodinger qquation and an optimal configuration problem. Cal. Var. and PDE, 25(2006), 105-137.
  368. (with D'Aprile) Layered solutions for a semilinear elliptic system in a ball J. Diff. Eqns. 226(2006), 269-294.
  369. (with T. D'Aprile) Boundary Concentration in radial solutions for a system of semilinear elliptic equations Journal of London Mathematical Society 74(2006), no.2, 415-440.
  370. (with D'Aprile) Locating the boundary peaks of least-energy solutions to a singularly perturbed Dirichlet problem Annali della Scuola Normale Superiore di Pisa, Classe di Scienze, Vol. V (2006), 219-259.
  371. (with Juan D\'avila, Manuel del Pino, Monica Musso ) Singular limits of a two-dimensional boundary value problem arising in corrosion modelling Archive Rational Mechanical Analysis 182(2006), no.2, 181-221.
  372. (with M. del Pino) Collapsing steady states of the Keller-Segel system Nonlinearity 19(2006), no.3, 661-684.
  373. (with M. del Pino and M. Kowalczyk) Resonance and interior layers in an inhomogeneous phase transition model . SIAM J. Math. Anal., 38(2006), no.5, 1542-1564.
  374. (with P. Esposita and A. Pistoia) Concentrating solutions for Henon equation in R^2 J' Analyse Math. 100(2006), 249-280.
  375. (with T. Kolokolnikov and M. J. Ward) Zigzag and breakup instabilities of stripes and rings for the two-dimensional Gray-Scott model. Studies in Applied Math. 116(2006), no.1, 35-95.
  376. (with T. Kolokolnikov, Thomas Erneux) Mesa-type patterns in the one-dimensional Brusselator and their stability Physica D: Nonlinear Phenomena 214(2006), no.1, 63-77.
  377. (with T. Kolokolnikov, M. Ward) Slow translational instabilities of spike patterns in the one-dimensional Gray-Scott model Interfaces and Free Boundaries 8(2006), no.2, 185-222.
  378. (with T. Kolokolnikov, M. Ward) The Stability of A Stripe for the Gierer-Meinhardt Model and the Effect of Saturation SIAM J. Applied. Dynamical Systems 5(2006), no.2, 313-363.
  379. (with ZM Guo) Hausdorff Dimension of Ruptures for Solutions of a Semilinear Elliptic Equation with Singular Nonlinearity Manuscripta Mathematica 120(2006), 193-209.
  380. (with T.C. Lin) Spikes in Two-component Systems of Nonlinear Schr\"{o}dinger Equations with Trapping Potentials Journal of Differential Equations 229(2006), no.2, 538-569.
  381. (with TC Lin) Solitary and Self-similar Solutions of Two-component System of Nonlinear Schr\"{o}dinger Equations . Physica D: Nonlinear Phenomena 220(2006), no. 2, 99-115
  382. (with TC Lin) Symbiotic bright solitary wave solutions of coupled nonlinear Schroedinger equations . Nonlinearity 19(2006), no.12, 2755-2773.
  383. (with M. Musso) Stationary Solutions to a Keller-Segel Chemotaxis System Asymptotic Analysis, 49(2006), no.3-4, 217-247.,
  384. (with W.-M. Ni) On positive solutions concentrating on spheres for the Gierer-Meinhardt system J. Diff. Eqns. 221(2006), 158-189.
  385. (with X. Ren) Droplet Solutions in the Diblock Copolymer Problem with Skewed Monomer Composition Cal. Var. and Part. Diff. Eqns. 25(2006), no.3, 333-359.
  386. (with Xiaofeng Ren) Existence and Stability of Spherically Layered Solutions of the Diblock Copolymer Equation SIAM J. Appl. Math. 66(2006), 1080-1099.
  387. (with M. Winter) Standing waves in the FitzHugh-Nagumo system and a problem in combinatorial geometry Math. Zeit 254(2006), no.2, 359-383.
  388. (with S. Yan) Solution Explosant Au Centre Et Le Long Du Bord Pour Un Probl\`{e}me Elliptique De Neumann Avec Non-Lin\'{e}arit\'e Critique . C. R. Acad. Sci. Paris, 343(2006), no.5, 311-316.
  389. (with D. Ye and F. Zhou) Bubbling Solutions for an Anisotropic Emden-Fowler Equation Comp. Rend. Acad. Sci. Paris 343(2006), no.4, 253-258.

    390. 2005

  390. (with Wenyi Chen) On Brezis-Nirenberg Problem on $\Sn^3$ and A Conjecture of Bandle-Benguria Com. Rend. Acad. Sci. Paris 341(2005), no.3, 153-156.
  391. (with M. del Pino and M. Kowalczyk) Nonlinear Schr\"odinger equations: Concentration on weighted geodesics in the semi-classical limit Comp. Rend. Acad. Sci. Paris 341(2005), no. 4, 223-228.
  392. (with T. D'Aprile) On bound states concentrating on spheres for the Maxwell-Schrodinger Equation SIAM J. Math. Anal. 37(2005), no. 1, 321-342.
  393. (with Theo Kolokolnikov) On ring-like solutions for the Gray-Scott model: existence, instability and self-replicating rings Eur. J. Appl. Math., 16(2005), no.2, 201-237.
  394. (with Theo Kolokolnikov and M.J.Ward) Pulse-splitting for some reaction-diffusion systems in one-space dimension, Studies in Appl. Math. 114(2005), no.2, 115-165.
  395. (with Theo Kolokolnikov and M. Ward) The existence and stability of spike equilibria in the one-dimensional Gray-Scott model: the pulse-splitting regime. Physica D: Nonlinear Phenomenon 202(2005), 258-293.
  396. (with Theo Kolokolnikov and M.J.Ward) The existence and stability of spike equilibria in the one-dimensional Gray-Scott model, Appl. Math. Letters, 18(2005), no. 8, 951-956.
  397. (with Theo Kolokolnikov and M. Ward) The existence and stability of spike equilibria in the one-dimensional Gray-Scott model: the low feed-rate regime. Studies in Appl. Math. 115(2005), no.1, 21-71.
  398. (with M.E. Hubbard and J. A. Leach) Pattern formation in a two-dimensional simple chemical system with general orders of autocatalysis and decay. IMA J. Appl. Math., 70(6)(2005), 723-747.
  399. (with T.-C. Lin) Spikes in two coupled nonlinear Schrodinger equations . Ann. Non linearie, Annoles de l'Institut H. Poincare, 22(2005), no. 4, 403-439.
  400. (with T.-C. Lin) Ground state of $N$ coupled Nonlinear Schr\"{o}dinger Equations in $R^n, n\leq 3$ Communications in Mathematical Physics 255(3)(2005), 629-653.
  401. (with W.-M. Ni and A. Malchiodi) Multiple clustered layer solutions for semilinear Neumann problems on a ball, Ann. Non linearie, Annoles de l'Institut H. Poincare 22(2005), 143-163.
  402. (with O. Rey) Blowing up Solutions for an Elliptic Neumann Problem with Sub- or Supercritical Nonlinearity. Part II: $N \geq 4$, Ann. Non linearie, Annoles de l'Institut H. Poincare, 22(2005), no. 4, 459-484.
  403. (with O. Rey) Arbitrary Number of Positive Solutions For an Elliptic Problem with Critical Nonlinearity. Journal of European Mathematical Society 7(2005), no. 4, 449-476.
  404. (with X. Ren) Wriggled lamellar solutions and their stability in the Diblock copolymer problem , SIAM J. Math. Anal. 37(2005), no.2, 455-489.
  405. (with Xiaofeng Ren) Nucleation in the FitzHugh-Nagumo System: Interface-Spike Solutions Journal of Differential Equations 205(2005), 266-301.
  406. (with B.D. Sleeman and M.J.Ward) The existence, stability, and dynamics of spike patterns in a chemotaxsis model , SIAM J. Appl. Math., 65(2005), no. 3, 790-817.
  407. (with Tobias Weth) On the Number of Nodal Solutions to a Singularly Perturbed Neumann Problem Manuscripta Mathematica 117(2005), no. 3, 333-344.
  408. (with M. Winter) On a cubic-quintic Ginzburg-Landau equation with global coupling, Proceedings of Amer. Math. Soc. 133(2005), no. 6, 1787-1796.
  409. (with Matthias Winter) Clustered spots in the FitzHugh-Nagumo system Journal of Differential Equations, 213(2005), no.1, 121-145.
  410. (with M. Winter) Symmetry of nodal solutions for singularly perturbed elliptic problems on a ball, Indiana Univ. Math. Journal, 54(2005), no. 3, 707-741.
  411. (with M. Winter and W.K. Yeung) A higher-order energy expansion to two-dimensional singularly perturbed Neumann problems Asymptotic Analysis, 43(2005), no.1-2, 75-110.
  412. (with Xingwang Xu) Uniqueness and a priori estimates for some nonlinear elliptic Neumann equations in $R^3$ Pacific J. Math., 221(2005), no.1, 159-165.

    413. 2004

  413. (with D. Iron and M. Winter) Stability analysis of Turing patterns generated by the Schnakenberg model Journal of Math. Biology 49(2004), no.4, 358-390.
  414. (with O. Rey) Blowing up solutions for an elliptic Neumann problem with sub- or supercritical nonlinearity I: $N=3$, Journal of Functional Analysis 212(2004), no.2, 472-499.
  415. (with X. Ren) Molecular chirality and soliton-stripe pattern in liquid crystal films Nonlinearity 17(2004), Vol. 2, 617-632.
  416. (with X. Ren) The soliton-stripe pattern in the Seul-Andelman membrane Physica D:Nonlinear Phenomenon 188 (2004), no. 3-4, 277--291.
  417. (with X. Ren) Stability of spot and ring solutions of the Diblock copolymer equation Journal of Mathematical Physics 45(2004), no.11, 4106-4133.
  418. (with M. Winter) Asymmetric Patterns for the Gierer-Meinhardt system J. Math. Pures Appl. (9)83(2004), no.4, 433-476.
  419. (with M. Winter) On Gierer-Meinhardt system with saturation Comm. Contemp. Math. 6(2004), no.2, 259-277.
  420. (with M. Winter) Higher order expansions and spike locations Cal. Var. PDE 20(2004), 403-430.

    421. 2003

  421. (with H. Berestycki) On singular perturbation problems with Robin boundary condition, Annali Suola Norm. Sup. Pisa Cl.Sci. (5) Vol.II (2003), 199-230.
  422. (with del Pino and M. Kowalczyk) Multi-bump Ground States of the Gierer-Meinhardt system in $R^2$, Ann. Non linearie, Annoles de l'Institut H. Poincare 20(2003), 53-85.
  423. (with J. Leach) Pattern formation in a simple chemical system with general orders of autocatalysis and decay. I. Stability analysis. Physica D:Nonlinear Phenomena 3-4(180)2003, 185-209.
  424. (with C.S. Lin) Locating the peaks of solutions via the Maximum Principle II: A local version of the method of moving planes. Comm. Pure Appl. Math. 6(2003), 784-809.
  425. (with X. Ren) Triblock copolymer theory: ordered ABC lamellar phase. Journal of Nonlinear Sciences 13(2003), 175-208.
  426. (with X. Ren) Triblock copolymer theory: free energy, disordered phase and weak segregation, Physica D:Nonlinear Phenomena 178(2003), 103-117.
  427. (with X. Ren) On energy minimizers of the di-block copolymer problem. Interfaces and Free Boundaries 5 (2003), no. 2, 193-238.
  428. (with X. Ren) On the spectra of 3-D Lamellar solutions of the Diblock copolymer problem SIAM J. Math. Anal. 35(1)(2003), 1-32.
  429. (with X. Ren) Soliton-stripe patterns in the charged Langmuir monolayers Journal of Nonlinear Sciences 13 (2003), no. 6, 603-624.
  430. (with X. Sun, T. Tang and M. Ward) Numerical challenges for resolving spike dynamics for two one-dimensional reaction-diffusion systems, Studies in Appl. Math. 111 (1)(2003), 41-84.
  431. (with M.J.Ward) Hopf bifurcations and oscillatory instabilities of spike solutions for the one-dimensional Gierer-Meinhardt model. Journal of Nonlinear Sciences 13(2003), 209-264.
  432. (with M.J.Ward) Hopf bifurcations of spike solutions for the shadow Gierer-Meinhardt model Europ. J. Appl. Math. 14 (2003), 677-711.
  433. (with M. Winter) Asymmetric spotty patterns for the Gray-Scott model, Studies in Appl. Math. 110(2003), 63-102.
  434. (with M. Winter) A nonloal eigenvalue problem and the stability of spikes for reaction-diffusion systems with fractional reaction rates, Int. J. Bifur. Chaos 13 (6) (2003), 1529-1543.
  435. (with M. Winter) Existence and stability of multiple spot solutions for the Gray-Scott model in $R^2$, Physica D: Nonlinear Phenomena 176(2003), 147-180.
  436. (with M. Winter) Higher order energy expansions for some singularly perturbed Neumann problems, Comptes Rend de L' Acad. des Sci. I. Math. 337(2003), 37-42.
  437. (with M. Winter) Stability of monotone solutions for the shadow Gierer-Meinhardt system with finite diffusivity, Diff. Int. Eqns. 16(2003), 1153-1180.

    438. 2002

  438. (with Guofang Wang) Steady State Solutions Of A Reaction-Diffusion System Modeling Chemotaxis, Math. Nach. 233-234(2002), 221-236..
  439. (with Guofang Wang) On a conjecture of Wolansky, Nonlinear Analysis:TMA 48(2002), 927-937.
  440. (with S.-I. Ei) Dynamics of metastable localized patterns and its application to the interaction of spike solutions for the Gierer-Meinhardt systems in two spatial dimension, Japan J. Industr. Appl. Math. 19(2002), 181-226
  441. (with J. Norbury and M. Winter) Existence and stability of singular patterns in a Ginzburg-Landau equation coupled with a mean field, Nonlinearity 15(2002), 2077-2096.
  442. (with X. Ren) Concentrically layered energy equilibria of the di-block copolymer problem, Europ. J. Appl. Math. 13(2002), 479-496.
  443. (with M. Ward) Asymmetric Spike Patterns for the One-dimensional Gierer-Meinhardt System: Equilibria and Stability, Europ. J. Appl. Math. 13(2002), 283-320.
  444. (with M.-J. Ward ) The existence and stability of asymmetric spike patterns for the Schnakenberg model, Studies in Appl. Math. 109(2002), 229-264.
  445. (with M. Winter) Spikes for the Two-Dimensional Gierer-Meinhardt System: The Strong Coupl ing Case, J. Diff. Eqns. 178(2002), 478-518.
  446. (with M. Winter) Critical threshold and stability of cluster solutions for large reaction-diffusion systems in $R^1$, SIAM J. Math. Anal. 33(2002), 1058-1089.

    447. 2001

  447. Pattern formations in two-dimensional Gray-Scott model: existence of single-spot solutions and their stability, Physica D: Nonlinear Phenomena 148(2001), 1-2, 20-48.
  448. Uniqueness and critical spectrum of boundary spike solutions, Proc. Royal Soc. Edin. A 131(2001), 1457-1480.
  449. Multiple condensations for a nonlinear elliptic equation with sub-critical growth and critical behavior, Proc. Edinburgh Math. Soc. 44(2001), 631-660.
  450. (with J. Ai and K.S. Chou) Self-similar solutions for the anisotropic affine curvature shortening problem, Cal. Var. PDE 13 (2001), 311-337.
  451. (with D. Iron and M.J. Ward) The stability of spike solutions to the one-dimensional Gierer-Meinhardt model, Physica D.: Nonlinear Phenomena 150 (2001), no. 1-2, 25--62.
  452. (with G. Lu and X. Xu) On Conformally Invariant Equation $ (-\Delta u)^p u-K(x)u^{\frac{N+2p}{N-2p}}=0$ and Its Generalizations, Annali di Mathematica Pura ed Applicata 179(2001), 309-329.
  453. (with L. Ma) Convergence for a Liouville equation, Comment. Math. Helv. 76(2001), 506-514.
  454. (with M. Winter)Solutions for the Cahn-Hilliard equation with many boundary spike layers, Proc. Roy Soc Edinb A 131(2001), 185-204.
  455. (with M. Winter) Spikes for the Two-Dimensional Gierer-Meinhardt System: The Weak Coupling Case Journal of Nonlinear Sciences 6(2001), 415-458.
  456. (with M. Winter) On a Hypercycle System with Nonlinear Rate, Methods Appl. Anal. 8(2001), 257-278.
  457. (with L. Zhang) On a nonlocal eigenvalue problem, Annali della Scuola Normale Superiore di Pisa, Classe di Scienze, XXX (2001), 41-62.

    458. 2000

  458. On the effect of the domain geometry in a singularly perturb ed Dirichlet problem, Diff. Int. Eqns 13(2000), 15-45.
  459. On a nonlocal eigenvalue problem and its applications to point-condensations in reaction-diffusion systems, Int. J. Bifurcation and Chaos, Vol. 10 (6) (2000), 1485-1496.
  460. (with M. del Pino and Felmer ) On the role of distance function in some singular perturbation pr oblems, Comm. PDE 25(2000), 155-177.
  461. (with M. Del Pino and P. Felmer ) Mutiple peak solutions for some singular perturbation problems, Cal. Var. PDE. 10(2000), 119-134.
  462. (with M. Grossi, A. Pistoia) Existence of multipeak solutions for a semilinear Neumann problem via nonsmooth critical point theory, Cal. Var. & PDE 11(2000) 143-175.
  463. (with C. Gui) On a sharp Moser-Aubin-Onofri inequality for functions on $S^2 $ with symmetry, Pacific J. Math. 194(2000), 349-358.
  464. (with Gui and M. Winter) Mutiple boundary peak solutions for some singularly perturbed Neumann problems, Ann. Non linearie, Annoles de l'Institut H. Poincare, , 17(2000), 47-82.
  465. (with C. Gui) On multiple mixed interior and boundary peak solutions for some singularly perturbed Neumann problems, Can. J. Math. 52(2000), 522-538.
  466. (with Xiaosong Kang) On interacting bumps of semiclassical states of nonlinear Schr\"odinger equations, Adv. Diff. Eqns. Vol. 5 (2000), 899-928.
  467. (with G. Lu)On a Sobolev inequality with remainder terms, Proceedings of AMS 128(2000), 75-84.
  468. (with Xiaofeng Ren) On the multiplicity of solutions of two nonlocal variational problems, SIAM J. Math. Anal. 31(2000), 909-924.
  469. (with M. Winter) Multi-Interior-Spike solutions for the Cahn-Hilliard equation with arbitrarily many peaks, Cal. Var. PDE 10(2000), 249-289.
  470. (with M. Winter) On a two dimensional reaction-diffusion system with hypercyclical structure, Nonlinearity 13(2000), 2005-2032.

    471. 1999

  471. Point condensations of a model for fungal development, C. R. Acad. Sci. Paris 328(1999), 129-134.
  472. Existence, stability and metastability of point condensation patterns generated by Gray-Scott System Nonlinearity 12(1999), 593-616.
  473. On single interior spike solutions of Gierer-Meinhardt system: uniqueness, spectrum estimates, Europ. J. Appl. Math. 10(1999), 353-378.
  474. (with E.N.Dancer) On the location of spikes and profile of solutions with two sharp layers, J. Diff. Eqns. 157(1999), 82-101.
  475. (with M. del Pino and Felmer ) On the role of mean curvature in some singularly perturbed Neumann problems, SIAM J. Math. Anal. 31 (1999), 63-79.
  476. (with C. Gui) Mutiple interior peak solutions for some singularly perturbed Neumann problems, J. Diff. Eqns. 158(1999), 1-27.
  477. (with Xuefeng Wang) Shift and stability of ground states of a nonlinear Schr\"odinger equation outside a small insulated domain, J. Diff. Eqns. 154(1999), 73-95.
  478. (with Winter) Multiple-peak solutions for a wide class of sing ular perturbation problems, J. London Math. Soc. 59(2)(1999), 585-606.
  479. (with M. Winter) On the two dimensional Gierer-Meinhardt system with strong coupling, SIAM J. Math. Anal. 30(1999), 1241-1243.
  480. (with Xingwang Xu) Classification of solutions of high order conformally invariant equations, Math. Annalen 313(2)(1999), 207-228.

    481. 1998

  481. Asymptotic behavior of least-energy solutions of a semilinear Dirichlet problem involving critical Sobolev exponent, J. Math. Soc. of Japan , Vol 1 (1998), 139-153.
  482. On the interior spike layer solutions of a singularly perturbed semilinear Neumann problem, Tohoku Math. J. , Vol. 50 (2), 1998, 159-178.
  483. Conditions for two-peaked solutions of singularly perturbed elliptic equations, Manuscripta Mathematica , 96(1998), 113-136.
  484. On the interior spike layer solutions for some singular perturbation problems, Proc. Royal Soc. Edinburgh, Section A (Mathematics) , 128 (1998), 849-874.
  485. (with G. Cerami) Multiplicity of multiple interior spike solutions for some singularly perturbed Neumann problem, International Mathematics Research Notes , 12(1998), 601-626.
  486. (with E.N.Dancer) On the effect of domain topology in some singular perturbation problems, Topological Methods in Nonlinear Analysis 11(2) (1998), 227-248.
  487. (with M. Flucher) Asymptotic behavior of elliptic free boundary problem, Math. Zeit 228(1998), 683-703.
  488. (with G. Lu) On Nonlinear Schrodinger Equations With Totally Degenerate Potentials, C. R. Acad. Sci. Paris, , 326(1998), 691-696.
  489. (with E. Noussair ) On the existence and profile of nodal solutions of some singularly perturbed semilinear Neumann problem, Comm. Partial Diff. Eqns. , 23(1998), 793-816.
  490. (with W.-M. Ni and I. Takagi) On the location and profile of sp ike-layer solutions to singularly perturbed semilinear Dirichlet problems: intermediate solutions, Duke Math. J. 94 (1998), 597-618.
  491. (with M. Winter ) Stationary solutions of Cahn-Hilliard equation, Ann. Non linearie, Annoles de l'Institut H. Poincare 15 (1998), 459-492.
  492. (with M. Winter ) On the Cahn-Hilliard equations II: interior spike Layer solutions, J. Diff. Eqns. 148(1998), 231-267.
  493. (with M. Winter) On the stationary Cahn-Hilliard equation: Bubble solutions, SIAM Journal on Mathematical Analysis 29(1998), 1492-1518.
  494. (with Xingwang Xu) On Conformal Deformations of Metrics On $S^n$ J. Functional Analysis , 157(1998), 292-325.

    495. 1997

  495. On the boundary spike layer solutions of a singularly perturbed semilinear Neumann problem, J. Diff. Eqns, 134 (1997), 104-133.
  496. Exact Multiplicity for Some Nonlinear Elliptic Equations in Balls, Proc. Amer. Math. Soc., 125 (1997), No. 11, 3235-3242.
  497. (with Dancer) On the profile of solutions with two sharp layers to a singularly perturbed semilinear Dirichlet problem, Proc. Royal Soc. Edinburgh, Section A (Mathematics), 127 A(1997), 691-701.
  498. (with M. Flucher) Semilinear Dirichlet problem with nearly critical exponent, asymptotic location of hot spots, Manuscript. Math. 94 (1997), 337-346.
  499. (with G. Lu) On positive entire solutions to the Yamabe-type problem on the Heisenberg and stratified groups, Electronic Research Announcements of American Mathematical Society , 3(1997), 83-89.
  500. (with E. Noussair ) On the effect of domain geometry on the exist ence and profile of nodal solutions of some singularly perturbed semilinear Dirichlet problem, Indiana Univ. Math. J. , 46(1997), 1255-1272.

    501. 1996

  501. On construction of single-peak spiky solutions to singularly perturbed semilinear Dirichlet problems, J. Diff. Eqns. 129 (2) 1996, 315-333.
  502. Asymptotic behavior of a nonlinear fourth order eigenvalue problem, Comm. Part. Diff. Eqns. , 21 (1996), 1451-1468.
  503. (with X. Ren) Single-point condensation and least energy solutions, Proc. Amer. Math. Soc, 124 (1) 1996, 111-120.

    504. 1995

  504. (with W.-M. Ni) On the location and profile of spike-layer solutions to singularly perturbed semilinear Dirichlet problems, Comm. Pure Appl. Math. , 48(1995), 723-761.
  505. (with X. Ren) Counting peaks of solutions to some quasilinear elliptic equations with large exponent, J. Diff. Eqn., 117(1995), 28-55.
  506. (with X. Ren) Asymptotic behavior of least energy solutions to a two dimensional semilinear problem with mixed boundary condition, Nonlinear Analysis: Theory, Methods and Applications, 24(4) 1995, 587-6 04.
  507. (with X. Ren) On a semilinear equation in $R^{2}$ when the exponent approaches infinity, J. Math. Anal. Appl., 189(1995), 179-193.
  508. (with X. Wang) On the equation $ \Delta u + K(x) u^{\frac{n+2}{n-2} \pm \epsilon^{2}}=0$ in $ R^{n} $, Rendiconti Del Circolo Matematico Di Palermo , XLIV (1995), 1-37.

    509. 1994

  509. (with X. Ren) On a two dimensional elliptic problem with large exponent in nonlinearity, Trans. Amer. Math. Soc. , 343 (2) 1994, 749-763.

Publications in Proceedings of Conference or Special Volumes:

  1. On the effect of domain geometry and boundary geometry in some singular perturbation problems, Differential Equations and Applications (P. Bates ed.) , International Press, 1998,326-339.
  2. On the construction of interior spike layer solutions to a singularly perturbed semilinear Neumann problem, PARTIAL DIFFERENTIAL EQUATIONS:THEORY AND NUMERICAL SOLUTION , CRC Press LLC, 1998, 336-349.
  3. Existence and Stability of Spikes for the Gierer-Meinhardt System (99 Pages) HANDBOOK OF DIFFERENTIAL EQUATIONS, stationary partial differential equations, volume 5 (M. Chipot ed.) , Elservier. pp. 489-581.
  4. Geometrization Program of Semilinear Elliptic Equations 2010 ICCM Proceedings AMS/IP Studies in Advanced Mathematics
  5. An introduction to the finite and infinite dimensional reduction methods Geometric analysis around scalar curvatures, 35–118 Lect. Notes Ser. Inst. Math. Sci. Natl. Univ. Singap., 31, World Sci. Publ., Hackensack, NJ, 2016.
  6. Sharp stability of the logarithmic Sobolev inequality in the critical point setting Potentials and partial differential equations—the legacy of David R. Adams, 77–102, Adv. Anal. Geom., 8, De Gruyter, Berlin, [2023] ,
    7. .

Book

  1. (with M. Winter) Mathematical Aspects of Pattern Formation in Biological Systems Applied Mathematical Sciences Series, Vol. 189, Springer 2014 , ISBN: 978-4471-5525-6.

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