中国科学院数学与系统科学研究院
数学研究所
数学科学全国重点实验室
非线性泛函分析研讨班
Speaker: 李福义 教授（山西大学）
Inviter: 张志涛
Language: Chinese
Title: A local valley theorem and its applications to elliptic equations on bounded domains
Time & Venue：2026年7月14日（星期二） 10:00-11:00 南楼N818
Abstract: In this paper, we develop a general minimax framework for constrained variational problems, establish a local valley theorem for finding sign-changing critical points of functionals on constraint manifolds, and further give a positive answer to the question concerning the existence of sign-changing normalized solutions for constrained nonlinear elliptic boundary value problems on bounded domains. The abstract results can be applied to study the existence of sign-changing solutions for other constrained problems, and the results for nonlinear elliptic problems extend some existing results in the literature. The results presented here were joint work with Cui Zhang and Zhanping Liang.
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