含凹凸非线性项陈-西蒙斯-薛定谔方程基态解的存在性  

The Existence of Ground State Solutions for The Chern-Simons-Schrödinger Equations with Concave-convex Nonlinearities

作　　者：赵岩 邱懿鹏 徐声悦 肖迎迎 Zhao Yan;Qiu Yipeng;Xu Shengyue;Xiao Yingying(School of Mathematical Sciences,Jiangxi Science&Technology Normal University,Nanchang 330038,Jiangxi,P.R.China)

机构地区：[1]江西科技师范大学数学科学学院,江西南昌330038

出　　处：《江西科技师范大学学报》2024年第6期82-86,共5页Journal of Jiangxi Science & Technology Normal University

基　　金：江西省科学教育学会在校研究生课题项目(KXJYS151);江西省基础教育研究课题(SZUJKSX2024-1022);江西科技师范大学博士启动基金(2022BSQD13)。

摘　　要：本文探究了含凹凸非线性项的陈-西蒙斯-薛定谔方程基态解的存在性,利用变分法找到了在Pohozaev流形上的Cerami序列,并对其紧性进行了讨论,从而证明了含凹凸非线性项陈-西蒙斯-薛定谔方程基态解的存在性。This paper explores the existence of ground state solutions for the Chern-Schrödinger equations with concave-convex nonlinearities,while the Cerami sequence on the Pohozaev manifold is found by using the variational method,and its compactness is discussed.Thus,the existence of the ground state solutions of the Chern-Simons-Schrödinger equations with concave-convex nonlinearities is proved.

关 键 词：陈-西蒙斯-薛定谔方程 变分法 Cerami序列 Pohozaev流形 

分 类 号：O175.29[理学—数学]