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Ground states solutions for some non-autonomous Schrödinger-Bopp-Podolsky system
- Source :
- Electronic Journal of Qualitative Theory of Differential Equations, Vol 2022, Iss 51, Pp 1-29 (2022)
- Publication Year :
- 2022
- Publisher :
- University of Szeged, 2022.
-
Abstract
- In this paper we study the existence of ground states solutions for non-autonomous Schrödinger–Bopp–Podolsky system \begin{equation*} \begin{cases} -\Delta u + u +\lambda K(x)\phi u = b(x)|u|^{p-2}u & \text{in} \ \mathbb{R}^{3}, \\ -\Delta \phi + a^2\Delta^2\phi = 4\pi K(x) u^{2} & \text{in}\ \mathbb{R}^{3}, \end{cases} \end{equation*} where $\lambda>0, 20$ and ${\lim_{\vert{x}\vert \to +\infty}}b(x)=b_\infty >0$ and satisfying suitable assumptions, but not requiring any symmetry property on them. We show that the existence of a positive solution depends on the parameters $\lambda$ and $p$. We also establish the existence of ground state solutions for the case $3.18\approx\frac{1+\sqrt{73}}{3}
Details
- Language :
- English
- ISSN :
- 14173875
- Volume :
- 2022
- Issue :
- 51
- Database :
- Directory of Open Access Journals
- Journal :
- Electronic Journal of Qualitative Theory of Differential Equations
- Publication Type :
- Academic Journal
- Accession number :
- edsdoj.205eb15ab3e4bb1bce3c08815d7d1dc
- Document Type :
- article
- Full Text :
- https://doi.org/10.14232/ejqtde.2022.1.51