走向现代数学学术报告 - 常小军教授（No. 754)

题目：Normalized solutions of L^2-supercritical NLS equations on metric graphs

报告人：常小军 教授（东北师范大学）

时间：2024年12月13日 9:00

腾讯会议ID：132-389-780

报告摘要：In this talk, we are concerned with the existence of non-trivial bound states of prescribed mass for the $L^2$-supercritical nonlinear Schrodinger equation on metric graphs. In recent years, significant progress has been made regarding normalized solutions in the $L^2$-subcritical or critical case. However, the $L^2$-supercritical NLSE on metric graphs was essentially untouched. We will present some existence results on mountain pass type normalized solutions in the $L^2$-supercritical regime for NLSE on metric graphs. These results are derived from a new minimax theorem with Morse index information for constrained functionals, along with a blow-up analysis of bound states with prescribed mass and bounded Morse index.

报告人简介：常小军，东北师范大学教授，博士生导师，美国《数学评论》评论员。2009年6月博士毕业于吉林大学应用数学专业，2015年1月起任东北师范大学数学与统计学院教授，主要从事非线性泛函分析及其应用的研究，已在《Annales de l’Institut Henri Poincaré, Analyse Non Linéaire.》, 《Trans. Amer. Math.Soc.》,《J. Differential Equations》,《Nonlinearity》等国际专业期刊上发表论文三十余篇，主持国家自然科学基金面上项目3项（1项在研）与省部级项目多项。