Existence of positive ground state solutions of critical nonlinear Klein–Gordon–Maxwell systems
In this paper we study the following nonlinear Klein–Gordon–Maxwell system \begin{equation*} \begin{cases}-\Delta u+ [m_0^2-(\omega+\varphi)^2]u=f(u)&\text{in}~ \mathbb R^3,\\ \Delta \varphi=(\omega+\varphi)u& \text{in}~ \mathbb R^3, \end{cases} \end{equation*} where $0<\omega< m_0$....
| Published in: | Electronic Journal of Qualitative Theory of Differential Equations |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
University of Szeged
2022-09-01
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| Subjects: | |
| Online Access: | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=9833 |
| Summary: | In this paper we study the following nonlinear Klein–Gordon–Maxwell system
\begin{equation*}
\begin{cases}-\Delta u+ [m_0^2-(\omega+\varphi)^2]u=f(u)&\text{in}~ \mathbb R^3,\\
\Delta \varphi=(\omega+\varphi)u& \text{in}~ \mathbb R^3,
\end{cases}
\end{equation*}
where $0<\omega< m_0$. Based on an abstract critical point theorem established by Jeanjean, the existence of positive ground state solutions is proved, when the nonlinear term $f(u)$ exhibits linear near zero and a general critical growth near infinity. Compared with other recent literature, some different arguments have been introduced and some results are extended. |
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| ISSN: | 1417-3875 |