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Wang, Lixia
Electronic journal of qualitative theory of differential equations, 01/2019, Letnik: 2019, Številka: 40Journal Article
In this paper, we consider the following nonhomogeneous Klein–Gordon–Maxwell system \begin{align*} \begin{cases} - \Delta u +V(x)u-(2\omega+\phi)\phi u =f(x,u)+h(x), &x\in \mathbb{R}^3,\\ \Delta \phi =(\omega+\phi)u^2, \quad & x\in \mathbb{R}^3, \end{cases} \end{align*} where $\omega>0$ 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.
