报告题目：Gluing higher‑topological‑type semiclassical states for nonlinear Schroinger equations
时 间：2021年10月15日（星期五）上午9：30
地 点：腾讯ID:735314567
主 办：数学与统计学院、福建省分析数学及应用重点实验室、福建省应用数学中心（福建师范大学）、 福建师范大学数学研究中心
参加对象：感兴趣的老师和学生
报告摘要：In Chen and Wang (Calc Var Part Differ Equ 56:1–26, 2017), we show that, if $\epsilon>0$ is small enough, then there exists a sequence of semiclassical states of higher topological type localized at alocal minimum set of the potential $V$ for the semiclassicalnonlinear Schr\odinger equation
-\epsilon^2\Delta v+V(x)v=|v|^{p-2}v,\ v\in H^1(\mathbb{R}^N).
In this paper, we consider a situation where $V$ has multiple isolated localminimum sets. We show that as $\epsilon\rightarrow 0,$ there existmulti-bump solutions of this equation being concentrated at those given local minimum sets while at the same time each bump behaves as a higher topological typesolution in one local minimum set as aforementioned.Thus the multi-bump solutions given here are constructed by gluing a sum of higher topological type solutions localized in separated local minimal sets of the potential.
报告人简介：陈少伟，男， 于中科院数学与系统科学研究院获博士学位，现为华侨大学教授，主要从事非线性泛函分析及其应用方面的研究工作，已在《Calc Var Part Differ Equ》、《Siam JMA》等国内外著名的学术期刊上发表论文30多篇，主持和参与多项国家基金项目。