具有径向位势的Klein-Gordon-Maxwell系统解的存在性和多重性  

Existence and Multiplicity of Solutions for Klein-Gordon-Maxwell Systems with Radial Potentials

作　　者：孙歆 段誉 SUN Xin;DUAN Yu(College of Science,Guizhou University of Engineering Science,Bijie 551700,China)

机构地区：[1]贵州工程应用技术学院理学院,贵州毕节551700

出　　处：《数学的实践与认识》2024年第9期203-212,共10页Mathematics in Practice and Theory

基　　金：毕节市科学技术项目([2023]28,[2023]52)。

摘　　要：研究如下Klein-Gordon-Maxwell系统-Δu+V(|x|)u-(2ω+φ)φu=λQ(|x|)f(u),x∈R3,Δφ=(ω+φ)u2,x∈R3,其中ω>0是一个常数,λ>0,V,Q是径向函数,其在无穷远处可能是消失的或强制的.当f仅在原点附近满足局部条件时,利用变分方法证明了系统非平凡径向解的存在性和多重性,并得到系统的解关于参数λ的依赖性.完善了此系统解研究的已有结果.This article concerns the following Klein-Gordon-Maxwell system■whereω>0is a constant,λ>0,V,Q are radial functions,which can be vanishing or coercive at infinity.When f satisfies local assumptions just in a neighborhood of the origin,existence and multiplicity of nontrivial radial solutions can be proved via variational methods and the dependence on the parameterλ of the solution to the system can be obtained.Our result completes some recent works concerning research on solutions of this system.

关 键 词：Klein-Gordon-Maxwell系统 变分法 存在性 多重性 

分 类 号：O175[理学—数学]