Electronic Journal of Differential Equations, 
Vol. 2020 (2020), No. 01, pp. 1-17.

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

Authors: Yu Su (Anhui Univ. of Science and Tech., Huainan, Anhui, China)
         Haibo Chen (Central South Univ., Changsha, Hunan, China)
         Senli Liu  (Central South Univ., Changsha, Hunan, China)
         Xianwen Fang (Anhui Univ. of Science and Tech., Huainan, Anhui, China)

Abstract:
 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.
 
Submitted October 24, 2019. Published January 06, 2020.
Math Subject Classifications: 35B38, 35J47.
Key Words: Fractional Schrodinger-Poisson system; weighted Hardy potential;
           critical exponent.