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Bifurcation analysis of fractional Kirchhoff–Schrödinger–Poisson systems in $\mathbb R^3$
- Source :
- Electronic Journal of Qualitative Theory of Differential Equations, Vol 2024, Iss 3, Pp 1-17 (2024)
- Publication Year :
- 2024
- Publisher :
- University of Szeged, 2024.
-
Abstract
- In this paper, we investigate the bifurcation results of the fractional Kirchhoff–Schrödinger–Poisson system \begin{equation*} \begin{cases} M([u]_s^2)(-\Delta)^s u+V(x)u+\phi(x) u=\lambda g(x)|u|^{p-1}u+|u|^{2_s^*-2}u~~&{\rm in}~\mathbb{R}^3, \\ (-\Delta)^t \phi(x)=u^2~~&{\rm in}~\mathbb{R}^3, \end{cases} \end{equation*} where $s,t\in(0,1)$ with $2t+4s>3$ and the potential function $V$ is a continuous function. We show that the existence of components of (weak) solutions of the above equation bifurcates out from the first eigenvalue $\lambda_1$ of the problem $$(-\Delta)^s u+V(x)u=\lambda g(x)u\quad\mbox{in }\mathbb R^3.$$ The main feature of this paper is the inclusion of a potentially degenerate Kirchhoff model, combined with the critical nonlinearity.
Details
- Language :
- English
- ISSN :
- 14173875
- Volume :
- 2024
- Issue :
- 3
- Database :
- Directory of Open Access Journals
- Journal :
- Electronic Journal of Qualitative Theory of Differential Equations
- Publication Type :
- Academic Journal
- Accession number :
- edsdoj.4cd6db302a4443eb8363d4fe8740875a
- Document Type :
- article
- Full Text :
- https://doi.org/10.14232/ejqtde.2024.1.3