广州数学大讲坛第十六期

第一百六十讲——重庆师范大学尤松博士学术报告

题目：Least energy positive solutions of critical Schrodinger systems with mixed competition and cooperation terms

时间：2022年12月07日（周三）下午15：00-17：00

地点：腾讯会议（会议ID：530-308-517 密码202212）

报告人：尤松 博士

摘要：In this talk, we investigate the existence of least energy positive solutions to the Schrodinger system with critical exponent in high dimensions. We provide several sufficient conditions on the coefficients that ensure the existence of least energy positive solutions; these include the situations of pure cooperation, pure competition and coexistence of both cooperation and competition coefficients. Based on new energy estimates, we obtain the precise asymptotic behaviours of the nonnegative solutions in some situations which include an analysis of a phase separation phenomena. Besides, based on the results about the phase separation, we prove the existence of least energy sign-changing solution to the Brezis-Nirenberg problem in lower dimension.

报告人简介:

尤松博士，2020年博士毕业于兰州大学，2020年9月至2022年9月在清华大学从事博士后研究，2022年10月入职重庆师范大学，主要研究临界Schrodinger系统和临界Choquard系统正解的存在性及其渐近行为，相关成果发表在《J. Funct. Anal》、《Calc. Var. Partial Differential Equations》、《Topological Methods in Nonlinear Analysis》等国际数学期刊上。