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学术报告
学术报告
澳门新葡新京官方网站百年校庆澳门新葡新京系列学术报告之十九 北京师范大学唐仲伟教授报告通知
澳门新葡新京:蔡易??发布时间:2019-06-14?? 浏览次数:270

北京师范大学唐仲伟教授将于近日来访我校,做偏微分方程方向的报告,以下是报告信息,欢迎感兴趣的师生参加。

  

时间:2019616日(星期日)10:00-11:00

地点:格物楼503

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

摘要:In this talk, we consider the following nonlinear elliptic equation involving the fractional Laplacian with critical exponent: $$(-\Delta)^{s}u=K(x)u^{\frac{N+2s}{N-2s}}, ~u> 0 ~\textmd{in}~ {\Bbb R}^{N},$$ 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.

  

报告人概况:唐仲伟,北京师范大学教授,博士生导师。20047月从中国科学院数学与系统科学院获得博士学位,随后在北京师范大学数学科学学院工作。2007930-2009101日,作为洪堡学者在德国吉森大学访问两年。主要从事非线性分析及其在偏微分方程中的应用等方向的研究工作,比如薛定谔方程的稳态解的研究等。

  

  

  

  


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