Existence, multiplicity, and concentration of positive solutions for a quasilinear Choquard equation with critical exponent

In this paper, we consider the quasilinear Choquard equations -epsilon(2)Delta u + V(x)u - epsilon(2)u Delta u(2) = epsilon(u-N) integral R-N vertical bar u(y)vertical bar(P)/vertical bar x y vertical bar(u) dy vertical bar u(x)vertical bar(P-2) u(x) + vertical bar u vertical bar(22*-2) u, where epsilon > 0 is a parameter, 0 < mu < 2 < N, and p(N) < p < 4(N-mu)/N-2) with p(N) = max{4, 3N-2 mu+2/N-2}. Under suitable assumption on V, we research the existence, multiplicity, and concentration of positive solutions for the problem by a dual approach. Published under license by AlP Publishing.