一类带临界指数的Schr dinger-Poisson系统的正解的存在性  

Existence of Positive Solutionsfor a Class of Schr dinger-Poisson System with Critical Exponent

作　　者：廖家锋 陈清方 LIAO Jia-feng;CHEN Qing-fang(School of Mathematics&Information,China West Normal University,Nanchong Sichuan 637009,China;College of Mathematics Education,China West Normal University,Nanchong Sichuan 637009,China)

机构地区：[1]西华师范大学数学与信息学院,四川南充637009 [2]西华师范大学公共数学学院,四川南充637009

出　　处：《西华师范大学学报（自然科学版）》2023年第4期358-364,共7页Journal of China West Normal University(Natural Sciences)

基　　金：西华师范大学创新团队科研项目(CXTD2018-8);西华师范大学基本科研项目(18B015)。

摘　　要：Schr dinger-Poisson系统是由Schr dinger方程和Poisson方程耦合在一起所得,它具有很强的物理背景,主要用来研究微观物质在电场中的运动规律。本文考虑有界区域上一类带临界指数的Schr dinger-Poisson系统,利用山路定理和Ekeland变分原理,获得了该系统至少存在2个正解。Schr dinger-Poisson system is obtained by coupling Schr dinger equation and Poisson equation.With a strong physical background,it is mainly used to study the motion law of micro matter in electric field.In this paper,a class of Schr dinger-Poisson system with critical exponents on bounded domains is considered and two positive solutions are obtained by Mountain Pass Theorem and Ekeland variational principle.

关 键 词：Schr dinger-Poisson系统 临界指数 山路定理 EKELAND变分原理 正解 

分 类 号：O177.91[理学—数学]