一、题目：On critical Choquard equation with potential wel

二、主讲人：沈自飞  教授、博士生导师

三、时间：5月30日(周四)下午13:30-14:30 
四、地点：A4-305报告厅

摘要：In this paper we are interested in the following nonlinear Choquard equation$$-\Deltau+(\lambdaV(x)-\beta)u=\big(|x|^{-\mu}\ast|u|^{2_{\mu}^{\ast}}\big)|u|^{2_{\mu}^{\ast}-2}u\hspace{4.14mm}\mbox{in}\hspace{1.14mm} \mathbb{R}^N,$$where $\lambda,\beta\in\mathbb{R}^+$,$0< \mu0$ is a constant such that the operator $-\Delta +\lambda V(x)-\beta$ is non-degenerate, we prove the existence of ground state solutions which localize near the potential well int$V^{-1}(0)$ for $\lambda$ large enough and also characterize the asymptotic behavior of the solutions as the parameter $\lambda$ goes to infinity. Furthermore, for any $0< \beta<\beta_{1}$, we are able to prove the existence of multiple solutions by the lusternik-schnirelmann category theory, where $\beta_{1}$ is the first eigenvalue of $-\delta$ on $\omega$ with dirichlet boundary condition.

报告人简介：沈自飞，浙江诸暨人，中共党员，教授、博导。曾任浙江师范大学数学系副主任，数太阳成集团tyc122cc副院长。现为浙江师范大学学术期刊社副社长、学报（自然科学版）副主编、《中学教研》杂志主编，核心期刊《数学教育学报》董事会副董长。浙江省高校中青年学科带头人，省重点建设专业“数学与应用数学”专业负责人，基础数学硕士点负责人。