Multiple positive solutions for a Choquard equation involving both concave-convex and Hardy-Littlewood-Sobolev critical exponent

Abstract

In this paper, we consider a Choquard equation involving both concave-convex and Hardy-Littlewood-Sobolev critical exponent. By using the N ehari manifold, fibering maps and the Lusternik-Schnirelman category, we prove that the problem has at least cat(Ω)+ 1 distinct positive solutions.