Existence of high energy solutions for superlinear coupled Klein-Gordons and Born-Infeld equations

In this article, we study the system of Klein-Gordon and Born-Infeld equations -Δ u +V(x)u-(2ω+φ)φ u =f(x,u), x∈ R³, Δ φ+βΔ₄φ=4π(ω+φ)u², x∈ R³, where \(Δ_4φ=div(|∇φ|^2∇φ)$\), \(ω\) is a positive constant. Assuming that the primitive of \(f(x,u)\) is of 2-superlinear growth in \(u\) at infinity, we prove the existence of multiple solutions using the fountain theorem. Here the potential \(V\) are allowed to be a sign-changing function. For more information see https://ejde.math.txstate.edu/Volumes/2024/18/abstr.html