Jie Yang, Lintao Liu, Haibo Chen, Ground state solutions for fractional Choquard-Schrödinger-Poisson system with critical growth

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DOI: 10.23952/jnva.8.2024.1.04

Volume 8, Issue 1, 1 February 2024, Pages 67-93

Abstract. In this paper, we study the following fractional Schr\”{o}dinger-Poisson system
$(-\Delta)^{s}u+V(x)u+\phi u=(I_{\mu}*F(u))f(u)+|u|^{2_{s}^{*}-2}u,$ in $\mathbb{R}^{3},$
$(-\Delta)^{t}\phi=u^{2},$ in $\mathbb{R}^{3},$
where $0<s,t<1,\ 2(s+t)>3, \mu\in (s+t,3),\ s\in [\frac{3}{4},1),$ and $2_{s}^{*}=\frac{6}{3-2s}$ is the fractional critical Sobolev exponent. By using a monotonicity argument and the global compactness lemma, we obtain the existence of a ground state solution for this system.

How to Cite this Article:
J. Yang, L. Liu, H. Chen, Ground state solutions for fractional Choquard-Schrödinger-Poisson system with critical growth, J. Nonlinear Var. Anal. 8 (2024), 67-93.