• I am interested in constructing solutions to semilinear partial differential equations including the Yamabe Equation, Allen-Cahn equation, (magnetic) Ginzburg-Landau Equation (U(1)-Yang-Mills-Higgs model), and energy-critical heat equation. I am also interested in studying the stability and other properties of these solutions.

• I am interested in studying the best constant of some geometric inequalities such as Beckner's inequality, a higher order Moser-Trudinger inequality.

1. (With Y. Liu, J. Wei) Stable solutions of U(1)-Yang-Mills-Higgs Model in R^4, preprint.

2. (With J. Wei, X. Zeng and Q. Zhang) Co-existence of Type II blow-ups with multiple blow-up rates for five-dimensional heat equation with critical nonlinear boundary conditions, preprint.

3. (With C. Gui, T. Li and J. Wei) On sharp Beckner’s inequality for axially symmetric functions on S^6 and S^8, Advances in Mathematics 480 (2025), part A, Paper No. 110487. Article-Preprint

4. (With J. Andrade and J. Wei) Complete metrics with constant fractional higher order Q-curvature on the punctured sphere, The Journal of Geometric Analysis, 2023, 34(1), 6. Article-Preprint

5. (With T. Li and J. Wei) On sharp Beckner’s inequality for axially symmetric functions on S^4, Math Research Letters 31(2024), no.5, 1523-1550. Article-Preprint

6. (With R.Lyu) 2D Thin obstacle problem with data at infinity, preprint. 

1.  Stability of solutions to the U(1)-Yang-Mills-Higgs equation in R^4.

Jan 15, 2025, at National University of Singapore.

2. On sharp Beckner’s inequality for axially symmetric functions on S^4, S^6 and S^8.

June 1, 2024, at Scholars Symposium on Nonlinear Analysis at Wuhan University of Technology.

3. On sharp Beckner’s inequality for axially symmetric functions on S^4 and S^6.

Nov 3, 2023, at Ming Li Colloquium at Wuhan University of Technology.