4月26日 唐仲伟教授学术报告(数学与统计学院)

作者:时间:2019-04-25浏览:31设置

人:唐仲伟教授

报告题目:Solutions for conformally invariant fractional Laplacian equations with multi-bumps centered in lattices

报告时间:2019426日(周五)上午10:00-11:30

报告地点:静远楼204学术报告厅

主办单位:数学与统计学院、m.toutou228.com技术研究院

报告人简介:

唐仲伟,男,1976年生,2004年从中国m.toutou228.com院数学与系统m.toutou228.com研究院博士毕业后在北京师范大学工作至今,现为北京师范大学数学m.toutou228.com学院党委书记,教授,博士生导师,北京市数学会副理事长,主要研究方向为非线性偏微分方程及非线性分析,在2007年至2009年期间作为洪堡学者访问德国学生大学两年。

报告摘要:

In this talk, we consider the following nonlinear elliptic equation involving the fractional Laplacian with critical exponent:

 $$(-\Delta)^{s}u=K(x)u^{\frac{N+2s}{N-2s}}, ~u> 0 ~\textmd{in}~ {\BbbR}^{N},$$

where s\in (0,1) and N>2+2s, K>0 is periodic in $(x_{1},\ldots, x_{k})$ with $1\leq k<\frac{N-2s}{2}$. Under some natural conditions on $K$ near a critical point, we prove the existence of multi-bump solutions where the centers of bumps can be placed in some lattices in ${\Bbb R}^{k},$ including infinite lattices. On the other hand, to obtain positive solution with infinite bumps such that the  bumps  locate in lattices in ${\Bbb R}^{k},$ the restriction on $1\leq k<\frac{N-2s}{2}$ is in some sense optimal, since we can show that for $ k\geq\frac{N-2s}{2},$  no such solutions exist. This is a joint work with Dr. Miaomiao Niu and Dr.Lushun Wang.



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