Electronic Journal of Differential Equations, 
Vol. 2020 (2020), No. 130, pp. 1-17.

Title: Schrodinger-Poisson systems with singular potential and critical exponent
       
Authors: Senli Liu  (Central South Univ., Changsha, Hunan, China)
         Haibo Chen (Central South Univ., Changsha, Hunan, China)
         Zhaosheng Feng (Univ. of Texas Rio Grande Valley, Edinburg, TX, USA)

Abstract:
 In this article we study the Schrodinger-Poisson system
 $$\displaylines{
 -\Delta u +V(|x|)u+\lambda\phi u = f(u), \quad x\in\mathbb{R}^3, \cr
 -\Delta \phi =u^2, \quad x\in\mathbb{R}^3,
 }$$
 where V is a singular potential with the parameter $\alpha$ and the nonlinearity f
 satisfies critical growth. By applying a generalized version of Lions-type theorem and
 the Nehari manifold theory, we establish the existence of the nonnegative ground state
 solution when $\lambda=0$.
 By the perturbation method, we obtain a nontrivial solution to above system when
 $\lambda\neq 0$.

Submitted July 18, 2020. Published December 26, 2020.
Math Subject Classifications: 35J20, 35J75, 35Q55.
Key Words: Schrodinger-Poisson system; Lions-type theorem;
           singular potential; ground state solution; critical exponent.