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, &...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
University of Szeged
2024-01-01
|
| 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=10461 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | 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. |
|---|---|
| ISSN: | 1417-3875 |