Existence of nontrivial solutions of a class of Schrödingersystems

摘要: In this talk, we will discuss existence of ground states, existence and multiplicity of bound states, uniqueness of positive solutions of a system of N-coupled time-independent Schroedinger equations from nonlinear optics and Bose-Einstein condensates.This system of Schroedinger equations has a very plentiful structure and reveals a lot of new phenomena.

 


刘兆理，首都师范大学数学系主任，国家杰出青年基金获得者，教育部长江学者特聘教授。长期从事临界点理论及其应用研究，发展了下降流不变集方法，并将这一新方法成功地应用于非线性椭圆型微分方程理论，在解的存在性、解的个数、变号解的个数、变号解nodal域的个数等方面获得了一批新结果，解决了多个疑难问题。