Existence and multiplicity of solutions for Klein-Gordon-Maxwell systems with sign-changing potentials

In this paper, we study the following nonlinear Klein-Gordon-Maxwell system: {-Delta u+V(x)u-(2 omega+phi)phi u=f(x,u)+h(x)vertical bar u vertical bar(q-2)u, x is an element of R-3, Df=(omega+phi)u(2), x is an element of R-3, (P-lambda) where and are positive constants, V is a continuous function with negative infimum, q is an element of (1,2), h is an element of 2/L2-q(R-3) is a positive potential function. Under the classic Ambrosetti-Rabinowitz condition, nontrivial solutions are obtained via the symmetric mountain pass theorem and the mountain pass theorem. In our paper, the nonlinearity F can also change sign and does not need to satisfy any 4-superlinear condition. We extend and improve some existing results to some extent.