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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.

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