Speaker: Peng Shuangjie, Professor and Vice President of Central China Normal University

Date: April 13, 2023

Time: 18:30-19:30

Location: Tencent Meeting

Sponsor: Research Center for Mathematics and Interdisciplinary Sciences

Research Center for Nonlinear Expectation

Abstract:

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.

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https://www.view.sdu.edu.cn/info/1020/177579.htm