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Ground states solutions for some non-autonomous Schrödinger-Bopp-Podolsky system

Authors :
Chun-Rong Jia
Lin Li
Shang-Jie Chen
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