Electron. J. Differential Equations, Vol. 2018 (2018), No. 124, pp. 1-21.

Two solutions for nonhomogeneous Klein-Gordon-Maxwell system with sign-changing potential

Lixia Wang, Shangjie Chen

Abstract:
In this article, we study the nonhomogeneous Klein-Gordon-Maxwell system
$$\displaylines{ - \Delta u +\lambda V(x)u-K(x)(2\omega+\phi)\phi u =f(x,u)+h(x), \quad x\in \mathbb{R}^3,\cr \Delta \phi =K(x)(\omega+\phi)u^2, \quad x\in \mathbb{R}^3, }$$
where $\omega>0$ is a constant and $\lambda>0$ is a parameter. Using the Linking theorem and Ekeland's variational principle in critical point theory, we prove the existence of multiple solutions, under suitable assumptions that allow a sign-changing potential.

Submitted November 16, 2017. Published June 16, 2018.
Math Subject Classifications: 35B33, 35J65, 35Q55.
Key Words: Klein-Gordon-Maxwell system; mountain pass theorem; nonhomogeneous; Ekeland's variational principle.

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Lixia Wang
School of Sciences
Tianjin Chengjian University
Tianjin 300384, China
email: wanglixia0311@126.com}
Shangjie Chen
School of Mathematics and Statistics
Chongqing Technology and Business University
Chongqing 400067, China
email: chensj@ctbu.edu.cn

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