LAUSR

In this paper, we consider the following nonhomogeneous Klein–Gordon– Maxwell system{ −∆u + V(x)u− (2ω + φ)φu = f (x, u) + h(x), x ∈ R3, ∆φ = (ω + φ)u2, x ∈ R3, where ω > 0 is a constant, the primitive of the nonlinearity f is of 2-superlinear growth at infinity. The nonlinearity considered here is weaker than the local (AR) condition and the (Je) condition of Jeanjean. The existence of two solutions is proved by the Mountain Pass Theorem and Ekeland’s variational principle.