一类 Klein-Gordon-Maxwell 系统解的存在性和多重性

数学物理学报 ›› 2025, Vol. 45 ›› Issue (3): 756-766.

一类 Klein-Gordon-Maxwell 系统解的存在性和多重性

段誉,孙歆^*()

贵州工程应用技术学院理学院贵州毕节 551700

收稿日期:2024-08-13 修回日期:2025-01-13 出版日期:2025-06-26 发布日期:2025-06-20
通讯作者: *孙歆, E-mail:sunxinwan3612@163.com
基金资助:
毕节市科学技术项目([2023]28);毕节市科学技术项目([2023]52)

Existence and Multiplicity of Solutions to a Class of Klein-Gordon-Maxwell Systems

Duan Yu,Sun Xin^*()

College of Science, Guizhou University of Engineering Science, Guizhou Bijie 551700

Received:2024-08-13 Revised:2025-01-13 Online:2025-06-26 Published:2025-06-20
Supported by:
Bijie Scientific and Technological Program([2023]28);Bijie Scientific and Technological Program([2023]52)

摘要/Abstract

摘要：

研究如下 Klein-Gordon-Maxwell 系统$\begin{equation*} \begin{cases} -\Delta u+ V(x)u-(2\omega+\phi)\phi u=f(x,u)+K(x)|u|^{s-2}u, & x\in \mathbb{R}^{3},\\ \Delta \phi=(\omega+\phi)u^2, & x\in \mathbb{R}^{3}, \end{cases} \end{equation*}$其中 $\omega> 0$ 是一个常数, $ 1< s<2$. 当 $f$ 仅在原点附近满足局部条件时, 利用变分法和 Moser 迭代证明了系统解的存在性和多重性. 完善了此系统解研究的已有结果.

关键词: Klein-Gordon-Maxwell 系统, 变分法, Moser 迭代, 非平凡解

Abstract:

This article concerns the following Klein-Gordon-Maxwell system $\begin{equation*} \begin{cases} -\Delta u+ V(x)u-(2\omega+\phi)\phi u=f(x,u)+K(x)|u|^{s-2}u, & x\in \mathbb{R}^{3},\\ \Delta \phi=(\omega+\phi)u^2, & x\in \mathbb{R}^{3}, \end{cases} \end{equation*}$ where $\omega> 0$ is a constant. When $f$ satisfies local condition just in a neighborhood of the origin, existence and multiplicity of nontrivial solutions can be proved via variational methods and Moser iteration. Our result completes some recent works concerning research on solutions of this system.

Key words: Klein-Gordon-Maxwell system, variational methods, moser iteration, nontrivial solutions

中图分类号:

O175.25

段誉, 孙歆. 一类 Klein-Gordon-Maxwell 系统解的存在性和多重性[J]. 数学物理学报, 2025, 45(3): 756-766.

Duan Yu, Sun Xin. Existence and Multiplicity of Solutions to a Class of Klein-Gordon-Maxwell Systems[J]. Acta mathematica scientia,Series A, 2025, 45(3): 756-766.

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