数学与信息科学学院学术报告(20170616)
发布时间:2017-06-14 浏览次数:

题  目: Least energy solutions of fractional Schrod-

inger equations involving potential wells

时  间:2017年6月16(星期五)上午10:00

报告人:唐仲伟 教授(北京师范大学)

地  点:先骕楼数信学院三楼学术报告厅4-3344

 

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. Moreover, the potential behaves like a potential well when the parameter  is large. Using variational methods, combining Nehari methods, we prove that the equation has a least energy solution which, as the parameterlarge, localizes near the bottom of  the potential well. Moreover, if the zero set int  of V(x) includes more than one isolated component, then  will be trapped around all the isolated components. However, in Laplacian case when s=1, for  large, the corresponding least energy solution will be trapped around  only one isolated component and will become arbitrary small in other components of int . This is the essential difference with the Laplacian problems since the operator fractional is nonlocal.

 

个人简介:唐仲伟教授,北京师范大学数学科学学院书记,教授,博士生导师。主要从事非线性偏微分方程及其应用等领域的研究,特别是对非线性薛定谔方程及方程组作了系统的研究。先后主持参与面上项目,天元基金项目等6项国家自然科学基金,发表学术论文30余篇。2007年10月2009年9月在德国做洪堡学者,到访过德国、美国、韩国等多个国家。