1. Bifurcation analysis of fractional Kirchhoff–Schrödinger–Poisson systems in $\mathbb R^3$
- Author
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Linlin Wang and Yuming Xing
- Subjects
kirchhoff–schrödinger–poisson system ,global bifurcation ,first eigenvalue ,fractional laplacian ,the fixed point ,whole space ,Mathematics ,QA1-939 - 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.
- Published
- 2024
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