Time：14:00-15:00, Monday, August 18 2025
Venue: E4-233
Speaker：Yang Zhou, Chinese University of Hong Kong
Title: Concentrated solutions to nonlinear Schrӧdinger equations with very degenerate potentials
Abstract:
We study the singularly perturbating Schrӧdinger equations with potential function . We obtain a more accurate location for the concentrated points, the existence and the local uniqueness for positive -peak solutions when 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 -peak solutions by using local uniqueness of concentrated solutions. This is a joint work with Peng LUO, Shuangjie PENG and Kefan PAN.
