Existence of semiclassical ground state solutions for a generalized Choquard equation

In this paper, we study a generalized quasilinear Choquard equation -ε^p∆_pu+V(x)|u=ε<mml:mo stretchy="true" maxsize="5.2ex" minsize="5.2ex">(</mml:mo>∫R^N <mml:mfrac>Q(y)F(u(y))|</mml:mfrac><mml:mo stretchy="true" maxsize="5.2ex" minsize="5.2ex">)</mml:mo>Q(x)f(u) in R^N, where ∆_p is the p-Laplacian operator, 1<p<N, V and Q are two continuous real functions on R^N, 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.