Two solutions for a nonhomogeneous Klein–Gordon–Maxwell system
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&...
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| Format: | Article |
| Language: | English |
| Published: |
University of Szeged
2019-06-01
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| Series: | Electronic Journal of Qualitative Theory of Differential Equations |
| Subjects: | |
| Online Access: | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=7074 |
| Summary: | 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. |
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| ISSN: | 1417-3875 |