美国犹他州立大学王志强教授学术讲座12月28日下午
发布时间: 2017-12-26 访问次数: 220

学术讲座Concentration of nodal solutions for nonlinear Schrödinger equations

时间2017122814:30 – 15:20

地点:旗山校区理工北楼601报告厅

主办:数学与信息学院、福建省分析数学及应用重点实验室、数学研究中心

主讲:美国犹他州立大学王志强

专家简介王志强教授,美国犹他州立大学终生教授,现受聘天津大学教授、中组部“千人计划”。在Morse理论应用于椭圆边值问题,椭圆问题的单峰解、多峰解、奇异变分问题、非线性Schrodinger方程和Schrodinger方程组等不失去紧性的变分问题的研究,取得了很多重要的研究成果,是国际著名的非线性分析和偏微分方程专家。

报告摘要We discuss the existence of localized sign-changing solutions for the semi-classical nonlinear Schrödinger equation with the potential V assumed to be bounded and bounded away from zero. When V has a local minimum point P, as, we construct an infinite sequence of localized sign-changing solutions clustered at P and these solutions are of higher topological type in the sense that they are obtained from a minimax characterization of higher dimensional symmetric linking structure via the symmetric mountain pass theorem. Our method combines the Byeon and Wang’s penalization approach and minimax method via a variant of the classical symmetric mountain pass theorem, and is rather robust without using any non-degeneracy conditions.