次线性Klein-Gordon-Maxwell系统解的多重性  

Multiplicity of Solutions for Sublinear Klein-Gordon-Maxwell Systems

作　　者：孙歆 段誉 Sun Xin;Duan Yu(College of Science,Guizhou University of Engineering Science,Guizhou Bijie 551700)

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：《数学物理学报（A辑）》2024年第5期1205-1215,共11页Acta Mathematica Scientia

基　　金：国家自然科学基金(11661021);毕节市科学技术项目([2023]28,[2023]52)。

摘　　要：该文研究如下Klein-Gordon-Maxwell系统{-Δu+u-(2ω+φ)φu=λQ(x)f(u),x∈R^(3)△φ=(ω+φ)u^(2),x∈R^(3)其中ω>0是一个常数,λ>0是一个参数,Q是一个正的函数.当非线性项f在无穷远处是次线性增长时,利用变分方法及三临界点定理获得此系统至少存在两个非平凡解.另外,当f仅在原点附近满足次线性增长时,利用变分方法及临界点定理获得此系统解的存在性及多重性.完善了此系统解的多重性的已有结果.This article concerns the following Klein-Gordon-Maxwell system{-Δu+u-(2ω+φ)φu=λQ(x)f(u),x∈R^(3)△φ=(ω+φ)u^(2),x∈R^(3),where w>O is a constant,λ>O is a parameter,Q is a positive function.When the nonlinear term f is sublinear at infinity,two nontrivial solutions for the system are established via variational methods and three critical points theorem.Furtermore,when f is sublinear only in a neighbourhood of the origin,existence and multiplicity of non-trivial solutions are obtained via variational methods and critical point theorem.Our result completes some recent works concerning the multiplicity of solutions of this system.

关 键 词：Klein-Gordon-Maxwell系统 变分法 次线性 临界点定理 多重性 

分 类 号：O175.25[理学—数学]