中国科学院数学与系统科学研究院
数学研究所
数学科学全国重点实验室
非线性泛函分析研讨班
Speaker: 雷春雨 副教授（贵州民族大学）
Inviter: 张志涛
Language: Chinese
Title: Ground states of the Schrodinger-Poisson Slater equations
Time & Venue: 2026年7月21日（星期二）10:00-11:00 南楼N818
Abstract: This talk is concerned with the Schrodinger-Poisson-Slater (SPS) equation with double critical exponents. Such exponents appear in the Coulomb-Sobolev inequality, and one is the Sobolev exponent and the other is called the Coulomb exponent here. We study the existence of nontrivial solutions of the SPS equation. This can be done by solving a variational problem with lack of compactness which is caused by those two critical exponents. Although the concentration compactness principle can be used to deal with the lack of compactness caused by the Sobolev exponent, it seems difficult to handle the other lack of compactness caused by the Coulomb exponent. In addition, we discuss the equivalent conditions for ground states obtained to the SPS equation.
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