报告题目：Prescribed mass solutions and limiting profiles for Schrodinger equations with critical exponents and lack of compactness

报告人：张建军教授，重庆交通大学

报告时间：2024年11月20日（周三）14:00-15:00

报告地点：腾讯会议ID: 571-763-407

报告摘要：We are concerned with the existence and multiplicity of prescribed mass positive solutions to Schrodinger equations with general critical nonlinearity, in particular, in the pure mass supercritical case and the mass mixed critical case. Precisely, for the pure mass supercritical case, under related mild assumptions, the existence of mountain pass normalized solutions is obtained for all prescribed mass $c>0$. We also capture its precise asymptotic behavior as $c$ goes to zero as well as $c$ goes to infinity. For the mass mixed case, there exist at least two different positive normalized solutions for small $c>0$. One is a local minimizer and the other one is a mountain pass solution. We also establish a sequence of properties for the local minimizer including the uniqueness and asymptotic behavior, etc. The asymptotic behavior of the mountain pass solution as $c\rightarrow 0^$ is also studied. Our results solve a sequence of open problems proposed by Soave( J. Funct. Anal., 279(6):108610, 2020).

报告人简介：张建军，重庆交通大学教授、清华大学博士，Mathematics Review评论员，2012年-2014年南开大学陈省身数学研究所博士后，2014年-2015年巴西帕拉伊巴联邦大学博士后，2015年-2016年和2018年-2019年意大利因苏布里亚大学博士后，2018年7月获得意大利副教授国家资格认证，主持国家自然科学基金-面上项目、国际（地区）合作交流项目、意大利伦巴第研究员基金（Global ERC）和中国博士后基金（二等）各一项，先后应邀访问美国、德国、意大利、葡萄牙，西班牙和巴西等多所研究机构，并多次在国际会议上作学术报告。研究领域主要包括非线分析中的变分与拓扑方法、非线性椭圆方程等，迄今已在包括Communications in Partial Differential Equations，Journal of Differential Equations, Calculus of Variations and Partial Differential Equations, Nonlinearity, Proceedings of the Royal Society of Edinburgh, Section A Mathematics，Journal of the London Mathematical Society, Annali di Matematica Pura ed Applicata, Communications in Contemporary Mathematics等刊物上发表SCI论文40余篇，其中ESI高被引4篇。

邀请人：非线性分析与PDE团队