勷勤数学•专家报告

题      目：Subcritical elliptic problem with the variable exponent

报  告  人：李本鸟 副教授  (邀请人：钟学秀)

                                              江西师范大学

时      间： 11月8日  11：00-12:00

地     点：数科院西楼二楼会议室

报告人简介:

          李本鸟，江西师范大学副教授，博士毕业于University of New England. 主要研究方向是非线性椭圆微分方程爆破解及集中解的性质，如存在性、唯一性、非退化性等。在Ann. Sc. Norm. Super. Pisa Cl. Sci.，Calc. Var. PDE，J. Differential Equations，Comm. Contem. Math.， Sci. China Math.等国际知名学术期刊上发表多篇学术论文。主持国家自然科学基金项目3项。

摘      要：

        In this talk, I will introduce some results about the elliptic problems with the variable exponent. At first, we study the nonlinear Schrödinger equation. Under suitable assumptions on the potentials, we prove, by the Lyapunov–Schmidt reduction method, that the equation admits infinitely many multi-bump solutions concentrating near the vertices of a regular polygon, with the number of bumps k serving as a parameter. Moreover, by combining local Pohozaev identities with blow-up analysis, we show that these solutions are non-degenerat. Then, we investigate the effect of a variable exponent on the nonlocal Schrödinger-Newton system. Using the Lyapunov-Schmidt reduction and Pohoz'aev identities, we establish the existence of a single-peak solution concentrating near a stable zero of an explicit vector field, together with its local uniqueness. These results reveal how the variable-exponent function and the potential affect the existence, multiplicity, non-degeneracy and uniqueness of solutions. This talk is based on the joint works with Yuke He, Wei Long and Minghui Rao.

          欢迎老师、同学们参加、交流！