理学院数理讲坛（2017年第18讲）
报告题目：Least energy solutions of fractional Schrodinger equations involving potential wells
报 告 人：唐仲伟 教授
单 位：北京师范大学
报告时间：2017年5月26日（星期五）15:30-16:30
报告地点：阳明学院303
报告摘要：In this talk, we study a class of nonlinear Schrodinger equations involving the fractional Laplacian. We assume that the potential of the equations includes a parameter $\lambda$. Moreover, the potential behaves like a potential well when the parameter $\lambda$ is large. Using variational methods, combining Nehari methods, we prove that the equation has a least energy solution which, as the parameter $\lambda$ large, localizes near the bottom of the potential well. Moreover, if the zero set int $V^{-1}(0)$ of $V(x)$ includes more than one isolated component, then $u_\lambda(x)$ will be trapped around all the isolated components. However, in Laplacian case when $s=1$, for $\lambda$ large, the corresponding least energy solution will be trapped around only one isolated component and will become arbitrary small in other components of int $V^{-1}(0)$. This is the essential difference with the Laplacian problems since the operator $(-\Delta)^{s}$ is nonlocal.
报告人简介：
唐仲伟，北京师范大学教授，博士生导师，数学科学学院党委书记。2004年从中国科学院数学与系统科学院获得博士毕业，并随后在北京师范大学数学科学学院工作，其中2007年9月-2009年10月：作为洪堡学者在德国吉森大学访问两年。主持国家自然科学基金面上基金和青年项目等多个国家课题。主要研究方向是非线性分析、椭圆偏微分方程，在多个国际高水平学术期刊上发表论文，如：JDE、 J. Fixed Theory Appl.、Discrete Contin. Dyn. Syst.、Pacific J. Math.等。