Two solutions for nonhomogeneous Klein-Gordon equations coupled with Born-Infeld type equations

• DOI: 10.58997/ejde.2022.74
• Publication Date: 2023-07-22T03:02:10Z
• Authors: Lixia Wang; Chunlian Xiong; Pingping Zhao
• Keywords: Variational principle; Constant (computer programming); Mountain pass theorem

This article concerns the nonhomogeneous Klein-Gordon equation coupled with a Born-Infeld type equation,$$\displaylines{- \Delta u +V(x)u-(2\omega+\phi)\phi =f(x,u)+h(x), \quad x\in \mathbb{R}^3,\cr \phi+\beta\Delta_4\phi=4\pi(\omega+\phi)u^2, \mathbb{R}^3, }$$ where \(\omega\) is positive constant. We obtain existence of two solutions using Mountain Pass Theorem, and Ekeland's variational principle in critical point theory.