华中师范大学彭双阶教授学术报告
题目：Singularly perturbed Schrodinger equations with very degenerate potentials.
报告人：彭双阶（华中师范大学，教授、副校长）
时间：2021年12月3日（周五），下午2:00-3:30
地点：腾讯会议，ID：296 229 059
摘要：This talk is related to a singularly perturbed nonlinear Schrodinger equation. We obtain a more accurate location for the concentrated points, the existence and the local uniqueness for positive peak solutions when the potential V(x) 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 lower dimensional ellipsoid, or a part of hyperboloid of one sheet or two sheets, we obtain the number and symmetry of k-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 V(x).
