Multi-bump solutions of Schrödinger–Bopp–Podolsky system with steep potential well
In this paper, we study the existence of multi-bump solutions for the following Schrödinger–Bopp–Podolsky system with steep potential well: \begin{equation*} \begin{cases} -\Delta u+(\lambda V(x)+V_0(x))u+K(x)\phi u= |u|^{p-2}u, &x\in \mathbb{R}^3,\\ -\Delta \phi+a^2\Delta^2\phi=K(x) u^2, &...
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University of Szeged
2024-01-01
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| Series: | Electronic Journal of Qualitative Theory of Differential Equations |
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| Online Access: | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=10461 |
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| author | Li Wang Jun Wang Jixiu Wang |
| author_facet | Li Wang Jun Wang Jixiu Wang |
| author_sort | Li Wang |
| collection | DOAJ |
| description | In this paper, we study the existence of multi-bump solutions for the following Schrödinger–Bopp–Podolsky system with steep potential well:
\begin{equation*}
\begin{cases}
-\Delta u+(\lambda V(x)+V_0(x))u+K(x)\phi u= |u|^{p-2}u, &x\in \mathbb{R}^3,\\
-\Delta \phi+a^2\Delta^2\phi=K(x) u^2, &x\in \mathbb{R}^3,
\end{cases}
\end{equation*}
where $p \in(4,6), a>0$ and $\lambda$ is a parameter. We require that $V(x) \geq 0$ and has a bounded potential well $\Omega=V^{-1}(0)$. Combining this with other suitable assumptions on $\Omega, V_{0}$ and $K$, when $\lambda$ is large enough, we obtain the existence of multi-bump-type solutions $u_{\lambda}$ by using variational methods. |
| format | Article |
| id | doaj-art-2a682290c4f04eabbe788b5369405de7 |
| institution | Kabale University |
| issn | 1417-3875 |
| language | English |
| publishDate | 2024-01-01 |
| publisher | University of Szeged |
| record_format | Article |
| series | Electronic Journal of Qualitative Theory of Differential Equations |
| spelling | doaj-art-2a682290c4f04eabbe788b5369405de72025-01-15T21:24:58ZengUniversity of SzegedElectronic Journal of Qualitative Theory of Differential Equations1417-38752024-01-0120241012210.14232/ejqtde.2024.1.1010461Multi-bump solutions of Schrödinger–Bopp–Podolsky system with steep potential wellLi Wang0Jun Wanghttps://orcid.org/0000-0003-0339-6808Jixiu Wang1East China Jiaotong University, Nanchang, ChinaDepartment of Mathematics, Sun Yat-sen University, Guangzhou, ChinaIn this paper, we study the existence of multi-bump solutions for the following Schrödinger–Bopp–Podolsky system with steep potential well: \begin{equation*} \begin{cases} -\Delta u+(\lambda V(x)+V_0(x))u+K(x)\phi u= |u|^{p-2}u, &x\in \mathbb{R}^3,\\ -\Delta \phi+a^2\Delta^2\phi=K(x) u^2, &x\in \mathbb{R}^3, \end{cases} \end{equation*} where $p \in(4,6), a>0$ and $\lambda$ is a parameter. We require that $V(x) \geq 0$ and has a bounded potential well $\Omega=V^{-1}(0)$. Combining this with other suitable assumptions on $\Omega, V_{0}$ and $K$, when $\lambda$ is large enough, we obtain the existence of multi-bump-type solutions $u_{\lambda}$ by using variational methods.http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=10461schrödinger–bopp–podolsky systempenalization methodvariational methods |
| spellingShingle | Li Wang Jun Wang Jixiu Wang Multi-bump solutions of Schrödinger–Bopp–Podolsky system with steep potential well Electronic Journal of Qualitative Theory of Differential Equations schrödinger–bopp–podolsky system penalization method variational methods |
| title | Multi-bump solutions of Schrödinger–Bopp–Podolsky system with steep potential well |
| title_full | Multi-bump solutions of Schrödinger–Bopp–Podolsky system with steep potential well |
| title_fullStr | Multi-bump solutions of Schrödinger–Bopp–Podolsky system with steep potential well |
| title_full_unstemmed | Multi-bump solutions of Schrödinger–Bopp–Podolsky system with steep potential well |
| title_short | Multi-bump solutions of Schrödinger–Bopp–Podolsky system with steep potential well |
| title_sort | multi bump solutions of schrodinger bopp podolsky system with steep potential well |
| topic | schrödinger–bopp–podolsky system penalization method variational methods |
| url | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=10461 |
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