一、报告题目

Concentrated solutions to nonlinear Schrodinger equations with very degenerate potentials

二、主讲人

彭双阶

三、报告时间

2023年4月13日18:30 – 19:30

四、报告地点

腾讯会议

五、摘要

We talk about a type of singularly perturbed nonlinear Schrodinger equation with a potential and obtain a more accurate location for the concentrated points, the existence and the local uniqueness for positive multi-peak solutions when the potential possesses non-isolated critical points by using the modified finite dimensional reduction method based on local Pohozaev identities. Moreover, for several special potentials, with its critical point set being a low-dimensional ellipsoid, or a part of hyperboloid of one sheet or two sheets, we obtain the number and symmetry of multi-peak solutions by using local uniqueness of concentrated solutions. Here the main difficulty comes from the different degenerate rate along different directions at the critical points of the potential. This is a joint work with Peng Luo, Kefan Pan and Yang Zhou.

六、主讲人简介

彭双阶，华中师范大学教授，副校长，国务院政府特殊津贴专家，教育部“新世纪优秀人才支持计划”、湖北省重大人才工程“高端人才引领培养计划”入选者。获得过教育部自然科学奖二等奖、湖北省自然科学奖一等奖和国家级教学成果二等奖。

彭双阶老师长期从事非线性偏微分方程、非线性泛函分析的研究，担任Comm.Pure.Appl.Anal.、Abs.Appl.Anal.编委、《数学物理学报》（中、英文版）常务编委、《应用数学学报》编委。在Arch. Ration. Mech. Anal., J. Math. Pure. Appl.,Adv. Math., Tran. Amer. Math. Soc.,Comm. PDEs, J. Funct. Anal.等国际顶尖期刊上发表论文100余篇.

七、主办单位

非线性期望前沿科学中心

数学与交叉科学研究中心