Bubbling/blow up analysis:

5. (with Guangzeng Yi) Blow up analysis for a parabolic MEMS problem, I: Hölder estimate, arXiv:2404.03223. (arXiv link)

4. (with Hua Chen and Jian-Meng Li), Blow up analysis for Keller-Segel system, arXiv:2210.12299. (arXiv link)

3. (with Juncheng Wei), Refined blowup analysis and nonexistence of Type II blowups for an energy critical nonlinear heat equation, arXiv:2101.07186. (arXiv link)

2. (with Juan Davila and Juncheng Wei), Qualitative analysis of rupture solutions for an MEMS problem, Annales de l'Institut Henri Poincare (C) Non Linear Analysis 33 (2016), no. 1,  221-242.  (arXiv link)

1. (with Juncheng Wei), Analysis of blow-up locus and existence of weak solutions for nonlinear supercritical problems, International Mathematics Research Notices 2015 (10), 2634-2670. 

 

Reaction-diffusion equation and travelling waves:

4. (with Hongjun Guo) Some new bistable transition fronts with changing shape, arXiv:2404.09237. (arXiv link)

3. Lipschitz property of bistable or combustion fronts and its applications, Journal de Mathématiques Pures et Appliquées 156 (2021), 215--244. 

2. (with Yihong Du, Changfeng Gui and Maolin Zhou), Semi-waves with $\Lambda$-shaped free boundary for nonlinear Stefan problems: Existence, Proceedings of the American Mathematical Society 149 (2021), 2091-2104.

1. (with Yihong Du and Hiroshi Matano), Regularity and asymptotic behavior of nonlinear Stefan problems, Archive for Rational Mechanics and Analysis 212 (2014), 957-1010.

 

Allen-Cahn equation:

14.  (with Zhuoran Du and Changfeng Gui), Four end solutions of a free boundary problem,Advances in Mathematics 404 (2022), Paper No. 108395, 39 pp.

13. (with Yong Liu and Juncheng Wei), Stability of the saddle solutions for the Allen-Cahn equation, arXiv:2001.07356. (arXiv link)

12. (with Changfeng Gui and Juncheng Wei), Axially symmetric solutions of Allen-Cahn equation with finite Morse index, Transactions of the American Mathematical Society 373 (2020), 3649-3668. (arXiv link)

11. (with Francois Hamel, Yong Liu, Pieralberto Sicbaldi and Juncheng Wei), Half space theorem for the Allen-Cahn equation and related problems, Journal fur die reine und angewandte Mathematik Vol. 2021, Issue 770, 113–133,  (arXiv link)

10. (with Juncheng Wei), Second order estimates on transition layers, Advances in Mathematics 358 (2019), 106856. (arXiv link)

9. (with Yong Liu and Juncheng Wei), On Smooth Solutions to One Phase-Free Boundary Problem in R^N, International Mathematical Research Notices 2021, no. 20, 15682-15732.  (arXiv link)

8. (with Vincent Millot and Yannick Sire), Asymptotics for the fractional Allen-Cahn equation and stationary nonlocal minimal surfaces, Archive for Rational Mechanics and Analysis, 231 (2019), no. 2, 1129-1216.  (arXiv link)

7. (with Juncheng Wei), Finite Morse index implies finite ends, Communication on Pure and Applied Mathematics 72 (2019), no. 5, 1044-1119.  (arXiv link)

6. (with Yong Liu and Juncheng Wei) On a free boundary problem and minimal surfaces, Annales de l'Institut Henri Poincare (C) Non Linear Analysis 35 (2018), no. 4, 993-1017.  (arXiv link)

5. (with Juncheng Wei) On Serrin's overdetermined problem and a conjecture of Berestycki, Caffarelli and Nirenberg, Communications in Partial Differential Equations 44 (2019), no. 9, 837-858.  (arXiv link)

4. (with Yong Liu and Juncheng Wei) Global minimizers of the Allen-Cahn equation in dimension n\geq 8, Journal de Mathmatiques Pures et Appliquees 108 (2017), no. 6, 818-840.  (arXiv link)

3. Some remarks on the structure of finite Morse index solutions to the Allen-Cahn equation in R^2, Nonlinear Differential Equations and Applications 24 (2017), 58.  (arXiv link)

2. The structure of finite Morse index solutions to two free boundary problems in R^2, arXiv preprint arXiv:1506.00491.  (arXiv link)

1. A new proof of Savin's theorem on Allen-Cahn equations, Journal of the European Mathematical Society 19 (2017), 2997-3051.  (arXiv link)

 

 

Stable and finite Morse index solutions:

9. (with Yong Liu, Kelei Wang, Juncheng Wei, Ke Wu) On Dancer's conjecture for stable solutions with sign-changing nonlinearity, arXiv:2312.00998. (arXiv link) 

8. (with Nikola Kamburov), Nondegeneracy for stable solutions to the one-phase free boundary problem, Mathematische Annalen 388 (2024), 2705–2726. (arXiv link)  

7. (with Yong Liu, Juncheng Wei and Ke Wu), Qualitative properties of stable solutions to some supercritical problems, Electronic Research Archive 30 (2022), no. 5, 1668--1690.

6. Recent progress on stable and finite Morse index solutions of semilinear elliptic equations, Electronic Research Archive 29 (2021), no. 6, 3805-3816.

5. Stable and finite Morse index solutions of Toda system, Journal of Differential Equations, 268 (2019), no. 1, 60-79.

4. (with Juan Davila, Louis Dupaigne and Juncheng Wei) A monotonicity formula and a Liouville-type theorem for a fourth order supercritical problem, Advances in Mathematics 258 (2014), 240-285.  (arXiv link)

3. (with Yihong Du and Zongming Guo) Monotonicity formula and varepsilon-regularity of stable solutions to supercritical problems and applications to finite Morse index solutions, Calculus of Variations and Partial Differential Equations 50 (2014), 615-638.

2. Partial regularity of stable solutions to the supercritical equations and its applications, Nonlinear Analysis: Theory, Methods and Applications 75 (2012), 5238-5260. Correction: Unfortunately there is a gap in the proof of Theorem 1.3 in this paper. It works only for p a little larger than the Joseph-Lundgren exponent in dimension n. The full theorem remains an open question.  

1. Partial regularity of stable solutions to the Emden equation, Calculus of Variations and Partial Differential Equations 44 (2012), 601-610. Erratum

 

 

Competing systems:

12. A generalized one phase Stefan problem as a vanishing viscosity limit, Portugaliae Mathematica 77 (2020), no. 2, 261–282. (arXiv link)

11. Uniform Lipschitz regularity of flat segregated interfaces in a singularly perturbed problem, Calculus of Variations and Partial Differential Equations 56 (2017), 135.  (arXiv link)

10. (with Juncheng Wei), On the uniqueness of solutions of an nonlocal elliptic system, Mathematische Annalen 365 (2016), no. 1, 105-153.  (arXiv link)

9. Harmonic approximation and improvement of flatness in a singular perturbation problem, Manuscripta Mathematica 146 (2015), no.1-2, 281-298.  (arXiv link)

8. The singular limit problem in a phase separation model with different diffusion rates, Discrete and Continuous Dynamical Systems-Series A 35 (2015), 483-512. 

7. On the De Giorgi type conjecture for an elliptic system modeling phase separation, Communications in Partial Differential Equations 39 (2014), 696-739.  (arXiv link)

6. (with Henri Berestycki, Susanna Terracini and Juncheng Wei), On entire solutions of an elliptic system modeling phase separations, Advances in Mathematics 243 (2013), 102-126.  (arXiv link)

5. Free boundary problems and asymptotic behavior of singularly perturbed partial differential equations, Springer Theses, Springer Berlin Heidelberg, 2013.

4. (with E. N. Dancer and Zhitao Zhang), The limit equation for the Gross-Pitaevskii equations and S. Terracini's conjecture, Journal of Functional Analysis 262 (2012), 1087-1131. Addendum

3. (with E. N. Dancer and Zhitao Zhang), Dynamics of strongly competing systems with many species, Transactions of the American Mathematical Society 364 (2012), 961-1005.

2. (with E. N. Dancer and Zhitao Zhang), Uniform Holder estimate for singularly perturbed parabolic systems of Bose-Einstein condensates and competing species, Journal of Differential Equations 251 (2011) 2737-2769.

1. (with Zhitao Zhang), Some new results in competing systems with many species, Annales de l'Institut Henri Poincare (C) Non Linear Analysis 27 (2010), 739-761.

 

 

Miscellaneous:

4. (with Hua Chen and Jian-Meng Li), On the vanishing viscosity limit of a chemotaxis model, Discrete and Continuous Dynamical System-Series A 40 (2020), no. 3, 1963-1987.

3. (with Juncheng Wei), On solutions with polynomial growth to an autonomous nonlinear elliptic problem, Advanced Nonlinear Studies 13 (2012), 921-932. (arXiv link)

2. (with Zhitao Zhang), On fixed point theorems of mixed monotone operators and applications, Nonlinear Analysis: Theory, Methods and Applications 70 (2009), 3279-3284.

1. (with Zhitao Zhang), Existence and non-existence of solutions for a class of Monge-Ampere equations, Journal of Differential Equations 246 (2009), 2849-2875.