騰訊會議ID：135 939 719
報告題目：Sharp weighted Sobolev inequality involving divergent operator with degeneracy and related sharp inequalities
報告摘要：In this talk we present the classification of all positive extremal functions to a sharp weighted Sobolev inequality on the upper half space, which involves divergent operators with degeneracy on the boundary. We show that such a weighted Sobolev inequality can be used to derive a sharp Sobolev type inequality involving Baouendi-Grushin operator, and deduce others weighted inequalities. This work joins with Liming Sun, Lei Wang and Meijun Zhu.
報告題目：Regularity, symmetry and asymptotic behavior of solutions for some integral systems
報告摘要：In this talk weintroduce some results about the positive solutions of some integral systems related to the static Hartree type equations. Firstly, assuming that the exponent p lying in some suitable interval depending on the parameters , we are able to prove some nonexistence results for the positive solution. Secondly, we also establish some qualitative results for the integrable solution of the system like regularity, symmetry and asymptotic behavior. As a corollary, we can get the corresponding results for the equivalent static Hartree type nonlocal equations.
騰訊會議ID：639 736 112
報告題目：Nonlocal problems with critical nonlinearities
報告摘要：In this talk, we mainly introduce some nonlocal problems with critical nonlinearities. By variational methods, we obtain the existence of solutions for the fractional Choquard Kirchhoff type problems with critical Hardy nonlinearities.
報告題目：Uniqueness of positive solutions with Concentration for the Schrdinger-Newton problem
報告摘要：We study the following Schodinger-Newton problem
For small enough, we show the uniqueness of positive solutions concentrating at the nondegenerate critical points of V(x). The main tools are a local Pohozaev type of identity, blow-up analysis and the maximum principle. Our results also show that the asymptotic behavior of concentrated points to Schrodinger-Newton problem is quite different from those of Schrodinger equations, which is mainly caused by the nonlocal term. This is a joint work with Peng Luo and Prof. Shuangjie Peng.