Normalized solutions of Sobolev critical Schrodinger equations in bounded domains

发布时间：2025-06-04 作者：浏览次数：

Speaker:	常小军	DateTime:	2025年6月6日（周五）下午15:00-16:00
Brief Introduction to Speaker: 常小军教授，东北师范大学		Place:	腾讯会议：584-368-643
Abstract:In this talk, we focus on the existence of positive normalized solutions of mountain pass type for Sobolev critical Schrodinger equations in bounded domains. In a recent paper by Pierotti, Verzini, and Yu (SIAM J. Math. Anal., 2025), it was proposed that for any bounded smooth domain, the nonlinear Schrodinger equations with Sobolev critical growth should admit a second positive normalized solution of mountain pass type, provided that the mass lies within a specific small interval. Our objective is to address this proposal. Our approach relies on a novel blow-up analysis for Sobolev-subcritical approximation solutions, with uniformly bounded Morse index and fixed mass.