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

Abstract

<p>In this article, we study the nonhomogeneous Klein-Gordon-Maxwell system</p> <pre>-∆u + λV(x)u - K(x) (2ω + φ) φu = ƒ(x, u) + h(x), x ∈ ℝ³,<br> ∆φ = K(x) (ω + φ)u², x ∈ ℝ³,</pre> <p>where ω > 0 is a constant and λ > 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.</p>