中科院数学与系统科学研究院

数学研究所

学术报告

非线性分析研讨班

报告人：田如顺 副教授（首都师范大学）

题  目：Multiple nontrivial solutions of a superlinear elliptic equation

时  间：2023.12.05（星期二）10:00-11:00

地  点：数学院南楼N802

摘  要：In this talk, we consider a superlinear elliptic equation with zero Dirichlet boundary condition. The nonlinearity f(x, u) has subcritical growth and satisfies the Ambrosetti-Rabinowitz condition. By assuming proper conditions on f(x, .) near the origin, togethering with Morse theory and minimax arguments, we obtain multiple nontrivial solutions. This result can be considered as a partial improvement of the paper by Chong Li and Shujie Li (Journal of Functional Analysis 271 (2016) 245--263. This is a joint work with Mingzheng Sun and Jiabao Su.

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报告人：张程翔 副教授（北京师范大学）

题  目：Nonlinear elliptic equations of sublinearity: qualitative behavior of solutions

时  间：2023.12.05（星期二）11:00-12:00

地  点：数学院南楼N802

摘  要：We study existence, uniqueness and qualitative property of solutions for a class of nonlinear elliptic equations of sublinearity. We also study the asymptotic behavior of ground state solution for sublinear equations in R^N and give estimates for radius of its support set as various parameters involved including the sublinearity power approaching to the limiting cases. This is a joint work with Profs. Norihisa Ikoma, Kazunaga Tanaka, and Zhi-Qiang Wang.