Existence of a ground state solution for Choquard equation with the upper critical exponent

Abstract

In this paper, we investigate the following Choquard equation −Δu+u=(Iα∗|u|N+αN−2)|u|N+αN−2−2u+g(u)inRN,where N⩾3,α∈(0,N), Iα is the Riesz potential and g is a given function. If g satisfies the general subcritical growth conditions, we obtain the existence of a positive ground state solution.