Groundstates for Choquard equations with the upper critical exponent

TL;DR

This paper establishes the existence of positive, radially symmetric groundstate solutions for a class of Choquard equations with the upper critical exponent using advanced variational methods.

Contribution

It extends previous results by applying the Pohozaev constraint and subcritical approximation methods to the critical Choquard equation.

Findings

Existence of positive, radially symmetric groundstates

Application of Pohozaev constraint method

Extension of earlier theorems on Choquard equations

Abstract

In this paper, an autonomous Choquard equation with the upper critical exponent is considered. By using the Poho\v{z}aev 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.