摘要：In this paper, we study the following nonlinear Klein–Gordon–Maxwell system: { − Δ u + V ( x ) u − ( 2 ω + ϕ ) ϕ u = f ( x , u ) + λ h ( x ) u q − 2 u , x ∈ R 3 , Δ ϕ = ( ω + ϕ ) u 2 , x ∈ R 3 , ( P λ ) $$ \textstyle\begin{cases} -\Delta u+ V(x)u-(2\omega +\phi )\phi u = f(x,u)+\lambda h(x) \vert u \vert ^{q-2}u, & x\in \mathbb{R}^",\\ \Delta \phi = (\omega +\phi )u^,, & x\in \mathbb{R}^", \end{cases}\displaystyle \quad (\mathrm{P_{\lambda }}) $$ where ω and λ are positive constants, V is a continuous function with negative infimum, q ∈ ( 1 , 2 ) $q\in (1,2)$ , h ∈ L 2 2 − q ( R 3 ) $h\in L^{\frac,{2-q}}(\mathbb{R}^")$ 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.
