Fractional Schrodinger-Poisson systems with weighted Hardy potential and critical exponent

In this article we consider the fractional Schrodinger-Poisson system $$\displaylines{ (-\Delta)^{s} u - \mu \frac{\Phi(x/|x|)}{|x|^{2s}} u +\lambda \phi u = |u|^{2^*_s-2}u,\quad \text{in } \mathbb{R}^3,\cr (-\Delta)^t \phi = u^2, \quad \text{in } \mathbb{R}^3, }$$ where \(s\in(0,3/4)\), \(t\in(0,1)...

Full description

Saved in:
Bibliographic Details
Published in:Electronic journal of differential equations 2020-01, Vol.2020 (1-132), p.1-17
Main Authors: Su, Yu, Chen, Haibo, Liu, Senli, Fang, Xianwen
Format: Article
Language:English
Subjects:
critical exponent
fractional schrodinger-poisson system
weighted hardy potential
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:In this article we consider the fractional Schrodinger-Poisson system $$\displaylines{ (-\Delta)^{s} u - \mu \frac{\Phi(x/|x|)}{|x|^{2s}} u +\lambda \phi u = |u|^{2^*_s-2}u,\quad \text{in } \mathbb{R}^3,\cr (-\Delta)^t \phi = u^2, \quad \text{in } \mathbb{R}^3, }$$ where \(s\in(0,3/4)\), \(t\in(0,1)\), \(2t+4s=3\), \(\lambda>0\) and \(2^*_s=6/(3-2s)\) is the Sobolev critical exponent. By using perturbation method, we establish the existence of a solution for \(\lambda\) small enough. For more information see https://ejde.math.txstate.edu/Volumes/2020/01/abstr.html
ISSN:1072-6691
1072-6691
DOI:10.58997/ejde.2020.01