School of Mathematics Sciences
China West Normal University
Nanchong Sichuan 637009, China
email: 2943658736@qq.com
School of Mathematics Sciences
China West Normal University
Nanchong, Sichuan 637009, China
email: liaojiafeng@163.com
Yu-Qin Zhao, Jia-Feng Liao
Abstract:
In this article, we study the fractional Kirchhoff-Schrodinger-Poisson
system with Sobolev critical growth
$$\displaylines{
\Big(a+b\int_{\mathbb{R}^3}|(-\Delta)^{s/2}u|^2dx\Big)
(-\Delta)^s u+ \phi u=\lambda u+ \mu|u|^{p-2}u+|u|^{2^*_s-2}u,
\quad \text{in }\mathbb{R}^3, \cr
(-\Delta)^s \phi=u^2, \quad \text{in }\mathbb{R}^3,
}$$
where \(a,b>0\), \(s\in(\frac{3}{4},1)\), \(p \in(2,2^*_s)\), and \(\mu >0\) is a parameter,
\(\lambda \in \mathbb{R}\) is an undermined parameter. For this problem, under the
\(L^2\)-subcritical, \(p\in(2, \frac{4s}{3}+2)\), we obtain the multiplicity of the
normalized solutions by means of the truncation technique, concentration-compactness
principle, and genus theory.
In the \(L^2\)-supercritical, \(p\in( \frac{8s}{3}+2, 2^*_s)\), we prove a couple
of normalized solutions by developing a fiber map and using the
concentration-compactness principle.
Submitted September 18, 2025. Published January 10, 2026.
Math Subject Classifications: 35B33, 35R11, 35J50.
Key Words: Kirchhoff-Schrodinger-Poisson system; normalized solution;
variational methods; L^2-subcritical; L^2-supercritical.
DOI: 10.58997/ejde.2026.03
Show me the PDF file (490 KB), TEX file for this article.
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Yu-Qin Zhao School of Mathematics Sciences China West Normal University Nanchong Sichuan 637009, China email: 2943658736@qq.com |
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Jia-Feng Liao School of Mathematics Sciences China West Normal University Nanchong, Sichuan 637009, China email: liaojiafeng@163.com |
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