Multiple solutions for superlinear Klein–Gordon–Maxwell equations†

Abstract

In this paper, we consider the following Klein–Gordon–Maxwell equations trueright84.0pt{−Δu+V(x)u−(2ω+ϕ)ϕu=f(x,u)+h(x)indouble-struckR3,−Δϕ+ϕu2=−ωu2indouble-struckR3,where ω>0 is a constant, u, ϕ:double-struckR3→R, V:double-struckR3→R is a potential function. By assuming the coercive condition on V and some new superlinear conditions on f, we obtain two nontrivial solutions when h is nonzero and infinitely many solutions when f is odd in u and h≡0 for above equations.

An improved result for a class of Klein–Gordon–Maxwell system with quasicritical potential vanishing at infinity

“…In [16], the authors investigated positive ground state solutions for a kind of fractional Klein‐Gordon‐Maxwell system. Very recently, Wu and Lin [19] obtained two nontrivial solutions for a class of nonhomogeneous Klein‐Gordon‐Maxwell system and improved the result of the related one in the literature by using some weak conditions.…”