Nonlocal Choquard equations involving critical Hardy-Littlewood-Sobolev exponent: the effect of the topology of the domain

TL;DR

This paper proves the existence of positive solutions for a class of nonlinear Choquard equations with critical exponents, using topological methods on bounded domains with nontrivial topology.

Contribution

It introduces a topological approach to establish solutions for Choquard equations involving critical Hardy-Littlewood-Sobolev exponents on domains with nontrivial homology.

Findings

Existence of positive solutions on certain bounded domains.

Application of topological methods to nonlinear PDEs.

Results depend on the domain's topological properties.

Abstract

We apply a topological method to prove existence of positive solutions for the nonlineair Choquard equation with upper critical exponent in the sense of Hardy-Littlewood-Sobolev inquality on bounded domains having nontrivial homology group.