On the existence and multiplicity of solutions for nonlinear Klein–Gordon–Maxwell system
In this paper, we study the existence and multiplicity solutions for the following Klein–Gordon–Maxwell system \begin{align*} \begin{cases} - \Delta u +V(x)u-(2\omega+\phi)\phi u =f(x,u), &x\in \mathbb{R}^3,\\ \Delta \phi =(\omega+\phi)u^2, \quad & x\in \mathbb{R}^3, \\ \end{cases} \en...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
University of Szeged
2023-05-01
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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=10072 |
| _version_ | 1797352363661459456 |
|---|---|
| author | Lixia Wang Chunlian Xiong Pingping Zhao |
| author_facet | Lixia Wang Chunlian Xiong Pingping Zhao |
| author_sort | Lixia Wang |
| collection | DOAJ |
| description | In this paper, we study the existence and multiplicity solutions for the following Klein–Gordon–Maxwell system
\begin{align*}
\begin{cases}
- \Delta u +V(x)u-(2\omega+\phi)\phi u =f(x,u), &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 and the nonlinearity $f(x,u)$ is either asymptotically linear in $u$ at infinity or the primitive of $f(x,u)$ is of 4-superlinear growth in $u$ at infinity. Under some suitable assumptions, the existence and multiplicity of solutions are proved by using the Mountain Pass theorem and the fountain theorem, respectively. |
| first_indexed | 2024-03-08T13:15:23Z |
| format | Article |
| id | doaj.art-76e0d9b7a39449d7996ca51cecb5382f |
| institution | Directory Open Access Journal |
| issn | 1417-3875 |
| language | English |
| last_indexed | 2024-03-08T13:15:23Z |
| publishDate | 2023-05-01 |
| publisher | University of Szeged |
| record_format | Article |
| series | Electronic Journal of Qualitative Theory of Differential Equations |
| spelling | doaj.art-76e0d9b7a39449d7996ca51cecb5382f2024-01-18T08:28:07ZengUniversity of SzegedElectronic Journal of Qualitative Theory of Differential Equations1417-38752023-05-0120231911810.14232/ejqtde.2023.1.1910072On the existence and multiplicity of solutions for nonlinear Klein–Gordon–Maxwell systemLixia Wang0Chunlian Xiong1Pingping Zhao2Tianjin Chengjian University, P.R. ChinaTianjin Chengjian University, P.R. ChinaTianjin Chengjian University, P.R. ChinaIn this paper, we study the existence and multiplicity solutions for the following Klein–Gordon–Maxwell system \begin{align*} \begin{cases} - \Delta u +V(x)u-(2\omega+\phi)\phi u =f(x,u), &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 and the nonlinearity $f(x,u)$ is either asymptotically linear in $u$ at infinity or the primitive of $f(x,u)$ is of 4-superlinear growth in $u$ at infinity. Under some suitable assumptions, the existence and multiplicity of solutions are proved by using the Mountain Pass theorem and the fountain theorem, respectively.http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=10072klein–gordon–maxwell systemsign-changing potential4-superlinearasymptotically linear |
| spellingShingle | Lixia Wang Chunlian Xiong Pingping Zhao On the existence and multiplicity of solutions for nonlinear Klein–Gordon–Maxwell system Electronic Journal of Qualitative Theory of Differential Equations klein–gordon–maxwell system sign-changing potential 4-superlinear asymptotically linear |
| title | On the existence and multiplicity of solutions for nonlinear Klein–Gordon–Maxwell system |
| title_full | On the existence and multiplicity of solutions for nonlinear Klein–Gordon–Maxwell system |
| title_fullStr | On the existence and multiplicity of solutions for nonlinear Klein–Gordon–Maxwell system |
| title_full_unstemmed | On the existence and multiplicity of solutions for nonlinear Klein–Gordon–Maxwell system |
| title_short | On the existence and multiplicity of solutions for nonlinear Klein–Gordon–Maxwell system |
| title_sort | on the existence and multiplicity of solutions for nonlinear klein gordon maxwell system |
| topic | klein–gordon–maxwell system sign-changing potential 4-superlinear asymptotically linear |
| url | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=10072 |
| work_keys_str_mv | AT lixiawang ontheexistenceandmultiplicityofsolutionsfornonlinearkleingordonmaxwellsystem AT chunlianxiong ontheexistenceandmultiplicityofsolutionsfornonlinearkleingordonmaxwellsystem AT pingpingzhao ontheexistenceandmultiplicityofsolutionsfornonlinearkleingordonmaxwellsystem |