Existence of semiclassical ground state solutions for a generalized Choquard equation

Abstract

In this paper, we study a generalized quasilinear Choquard equation−εpΔpu+V(x)|u|p−2u=εμ−N(∫RNQ(y)F(u(y))|x−y|μ)Q(x)f(u)in RN, where Δp is the p-Laplacian operator, 1<p<N, V and Q are two continuous real functions on RN, 0<μ<N, F(s) is the primate function of f(s) and ε is a positive parameter. Under suitable assumptions on p,μ 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.