Ground state solutions for Schrödinger–Poisson systems on ℝ3$$ {\mathbb{R}}^3 $$ with a weighted critical exponent

Abstract

In this paper, we are interested in the existence of ground state solutions for the weighted critical Schrödinger–Poisson systems. The weighted critical exponent may be the Hénon–Sobolev, the Sobolev or the Hardy–Sobolev critical exponent. Moreover, the potentials are power type, which may be singular at origin or unbounded. Due to the presence of Possion term, we can not directly obtain the boundedness of the Palais–Smale sequences of the associated functional for some cases. The Pohozaev identity, the minimax principle and some techniques are used to overcome the difficulties.