江苏省应用数学（中国矿业大学）中心系列学术报告
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
报告时间：2024年7月1日（周一）下午14:30-15:30
报告地点：数学学院A302
主持人：范海宁
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，重庆交通大学数学与统计学院教授，重庆市数学会副理事长，贵州大学博士生导师。2001年本科毕业于中国矿业大学数学系，2012年于清华大学数学科学系获博士学位，2018年获得意大利副教授国家资格认证，2020年入选重庆市高校中青年骨干教师，主持国家自然科学基金3项（面上项目2项）和意大利伦巴第研究员基金（Global ERC）1项。在非线性薛定谔方程的半经典状态和规范化解的研究等方面取得了一些结果，在JMPA，CPDE，CVPDE，JDE，Nonlinearity等刊物上发表多篇论文。