一类临界Schr?dinger方程的正基态径向解  

Positive Ground State Radial Solutions for a Class of Critical Schr?dinger Equation

作　　者：杜瑶 唐春雷[1] DU Yao;TANG Chun-Lei(School of Mathematics and Statistics ,Southwest University,Chongqing 400715,China)

机构地区：[1]西南大学数学与统计学院

出　　处：《西南师范大学学报（自然科学版）》2019年第6期22-26,共5页Journal of Southwest China Normal University(Natural Science Edition)

基　　金：国家自然科学基金项目(11471267);重庆研究生科研创新项目(CYS17084)

摘　　要：研究了径向空间中带有Sobolev临界指数的Schrodinger方程,不要求方程临界项带有的位势满足周期或渐近周期的相关条件.主要利用Nehari流形和Ekeland变分原理找到相应流形上的极小化序列,进而证明基态径向解的存在性.最后运用强极大值原理证明方程的解是正解,从而得到方程的正基态径向解.In this paper, a Schroinger equation with critical Sobolev exponent in the radial space has been studied, and the potential of critical term is not periodic or asymptotic periodic. Nehari manifold and Ekeland’s variational principle have been applied to find a sequence of minimizing sequence, moreover, the existence of ground state solutions has been proved. Finally, strong maximum principle implies the solution is positive. Therefore, the existence of a positive ground state radial solution is established.

关 键 词：SCHRODINGER方程 SOBOLEV临界指数 EKELAND变分原理 正基态径向解 

分 类 号：O176[理学—数学]