江蘇省應用數學（中國礦業大學）中心系列學術報告
報告題目：Prescribed mass solutions and limiting profiles for Schrodinger equations with critical exponents and lack of compactness
報告人：張建軍教授
報告時間：2024年7月1日（周一）下午14:30-15:30
報告地點：伟德bvA302
主持人：範海甯
報告摘要：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).
報告人簡介：張建軍，重慶交通大學數學與統計學院教授，重慶市數學會副理事長，貴州大學博士生導師。2001年本科畢業于中國礦業大學數學系，2012年于清華大學數學科學系獲博士學位，2018年獲得意大利副教授國家資格認證，2020年入選重慶市高校中青年骨幹教師，主持國家自然科學基金3項（面上項目2項）和意大利倫巴第研究員基金（Global ERC）1項。在非線性薛定谔方程的半經典狀态和規範化解的研究等方面取得了一些結果，在JMPA，CPDE，CVPDE，JDE，Nonlinearity等刊物上發表多篇論文。