Ground state solutions for nonlinear Choquard equation with singular potential and critical exponents

Abstract

In this paper, we study the ground state solutions to the following Choquard equation involving singular potential:−Δu+V(|x|)u=(Iα⁎F(u))f(u),x∈RN, where N⩾3, α∈(0,N), Iα is the Riesz potential, V is a singular potential with parameter θ∈(max⁡{0,4−N},2)∪(2,2N−2)∪(2N−2,∞), F is the primitive of f and f satisfies critical growth in sense of the Hardy-Littlewood-Sobolev inequality. Under different range of θ and almost necessary conditions on the nonlinearity f in the spirit of Berestycki-Lions type conditions, we divide this paper into three parts. By virtue of two different kinds of Lions-type theorem and Nehari manifold, some existence results are established.