Multiple positive solutions for nonhomogeneous Klein-Gordon-Maxwell equations

Abstract In this paper, we study the multiplicity of positive solutions for a class of nonhomogeneous Klein-Gordon-Maxwell equations { − Δ u + V ( x ) u − ( 2 ω + ϕ ) ϕ u = f ( x , u ) + h ( x ) , in R 3 , Δ ϕ = ( ω + ϕ ) u 2 , in R 3 , where ω is a positive constant. Under some suitable assumptions on V(x), f(x, u) and h(x), we prove the existence of two positive solutions by using the Ekeland’s variational principle and the Mountain Pass Theorem. These results improve the related ones in the literature.

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