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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| 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 |
| _version_ | 1826866518773727232 |
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| author | Linlin Wang Yuming Xing |
| author_facet | Linlin Wang Yuming Xing |
| author_sort | Linlin Wang |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-08T13:15:11Z |
| format | Article |
| id | doaj.art-4cd6db302a4443eb8363d4fe8740875a |
| institution | Directory Open Access Journal |
| issn | 1417-3875 |
| language | English |
| last_indexed | 2025-02-16T22:00:59Z |
| publishDate | 2024-01-01 |
| publisher | University of Szeged |
| record_format | Article |
| series | Electronic Journal of Qualitative Theory of Differential Equations |
| spelling | doaj.art-4cd6db302a4443eb8363d4fe8740875a2025-01-15T21:24:58ZengUniversity of SzegedElectronic Journal of Qualitative Theory of Differential Equations1417-38752024-01-012024311710.14232/ejqtde.2024.1.310670Bifurcation analysis of fractional Kirchhoff–Schrödinger–Poisson systems in $\mathbb R^3$Linlin Wang0Yuming XingSchool of Mathematics, Harbin Institute of Technology, Harbin, 150001, P.R. ChinaIn 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.http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=10670kirchhoff–schrödinger–poisson systemglobal bifurcationfirst eigenvaluefractional laplacianthe fixed pointwhole space |
| spellingShingle | Linlin Wang Yuming Xing Bifurcation analysis of fractional Kirchhoff–Schrödinger–Poisson systems in $\mathbb R^3$ Electronic Journal of Qualitative Theory of Differential Equations kirchhoff–schrödinger–poisson system global bifurcation first eigenvalue fractional laplacian the fixed point whole space |
| title | Bifurcation analysis of fractional Kirchhoff–Schrödinger–Poisson systems in $\mathbb R^3$ |
| title_full | Bifurcation analysis of fractional Kirchhoff–Schrödinger–Poisson systems in $\mathbb R^3$ |
| title_fullStr | Bifurcation analysis of fractional Kirchhoff–Schrödinger–Poisson systems in $\mathbb R^3$ |
| title_full_unstemmed | Bifurcation analysis of fractional Kirchhoff–Schrödinger–Poisson systems in $\mathbb R^3$ |
| title_short | Bifurcation analysis of fractional Kirchhoff–Schrödinger–Poisson systems in $\mathbb R^3$ |
| title_sort | bifurcation analysis of fractional kirchhoff schrodinger poisson systems in mathbb r 3 |
| topic | kirchhoff–schrödinger–poisson system global bifurcation first eigenvalue fractional laplacian the fixed point whole space |
| url | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=10670 |
| work_keys_str_mv | AT linlinwang bifurcationanalysisoffractionalkirchhoffschrodingerpoissonsystemsinmathbbr3 AT yumingxing bifurcationanalysisoffractionalkirchhoffschrodingerpoissonsystemsinmathbbr3 |