Existence of semiclassical ground state solutions for a generalized Choquard equation

In this paper, we study a generalized quasilinear Choquard equation -epsilon(p)Delta(p)u + V(x)vertical bar u vertical bar(p-2)u = epsilon(mu-N)(integral(RN)Q(y)F(u(y))/vertical bar x - y vertical bar(mu))Q(x)f(u) in R-N, where Delta(p) is the p-Laplacian operator, 1 < p < N, V and Q are two continuous real functions on R-N, 0 < mu < N, F(s) is the primate function of f(s) and epsilon is a positive parameter. Under suitable assumptions on p, mu and f, we establish a new concentration behavior of solutions for the quasilinear Choquard equation by variational methods. The results are also new for the semilinear case p = 2. (C) 2014 Elsevier Inc. All rights reserved.