Ground states for Choquard equations with doubly critical exponents

Abstract

In this paper, an autonomous Choquard equation with doubly critical exponents is studied. By using the Pohozaev constraint and the perturbed method, a positive and radially symmetric ground state solution in $H^1(\mathbb {R}^N)$ is obtained. The result here extends and complements the earlier theorems obtained by Seok and Moroz and Schaftingen.