学术报告会：A Generalized Mountain Pass Lemma with a Closed Subset for Locally Lipschitz Functionals

报告题目：A Generalized Mountain Pass Lemma with a Closed Subset for Locally Lipschitz Functionals

报 告 人：张世清   四川大学教授

报告时间：2023年9月17日周日下午4:00

报告地点：S3-313

摘要：The classical Mountain Pass Lemma of Ambrosetti-Rabinowitz has been studied, extended and modified in several directions. Notable examples would certainly include the generalization to locally Lipschitz functionals by K. C. Chang, analyzing the structure of the critical set in the mountain pass theorem in the works of Hofer, Pucci-Serrin and Tian, and the extension by Ghoussoub-Preiss to closed subsets in a Banach space with recent variations. In this talk, we utilize the generalized gradient of Clarke and Ekeland's variatonal principle to generalize the Ghoussoub-Preiss's Theorem in the setting of locally Lipschitz functionals. We give an application to periodic solutions of Hamiltonian systems.

个人简介：

张世清, 四川大学教授、博导, 1991在南开大学数学所获得博士学位。于 2002 年获教育部跨世纪人才基金, 作为项目主持人已获得 6 项国家自然科学 基金, 还参加了一项由北京大学张恭庆院士主持的国家自然科学基金重点项目, 主持过1项教育部优秀年轻教师基金和 2 项博士点基金。主要研究方向是微分方程及其应用，非线性泛函分析及其应用。已在Archiv. Rational Mech. Anal., SIAM J. Math. Anal., Annals of the New York Acade my of Sciences, J. of Differential Equations, Nonlinearity, Celestial Mechanics, Geometry and Physics, Discrete and Continuous Dynamical Systems-A, Science in China-A, Acta Mathematica Sinica-New Series等著名学术刊物发表论文多篇。其中与周青教授合作的论文中有两篇论文被法国著名数学家A. Chenciner 在 2002 年国际数学家大会报告( 1 卷校对补充稿) 中多次引用和高度评价。他与合作者的论文还被物理顶级综合刊物 Reports on Progress in Physics及天文学顶级综合刊物 The Astronomical Journal引用。有3篇论文被国际数学最顶尖杂志 Annals of Math. 引用。已在科学出版社出版著作一部“泛函分析及其应用”。曾应邀在英国 Warwick 大学及美国 Princeton 大学、Michigan 州立大学等近10所国外大学及国内多所著名大学做过学术报告。