Bifurcation analysis of fractional Kirchhoff–Schrödinger–Poisson systems in $\mathbb R^3$
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...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
University of Szeged
2024-01-01
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| 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=10670 |
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| Summary: | 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. |
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| ISSN: | 1417-3875 |