Groundstates for Choquard equations with the upper critical exponent

Abstract

In this paper, an autonomous Choquard equation with the upper critical exponent is considered. By using the Pohožaev constraint method, the subcritical approximation method and the compactness lemma of Strauss, a groundstate solution in $H^1({\mathbb{R}}^N)$ which is positive and radially symmetric is obtained. The result here extends and complements the earlier theorems.

References in corpus (1)

• Ground states and semiclassical states of nonlinear Choquard equations involving Hardy-Littlewood-Sobolev critical growth