Existence and Concentration Behavior of Ground States for a Generalized Quasilinear Choquard Equation Involving Steep Potential Well

In this paper, we consider the following generalized quasilinear Choquard equation with steep potential well −div(g2(u)∇u) + g(u)g (u)|∇u|2 + λV(x)u = (Iα ∗ F(u)) f (u), x ∈ RN , where N ≥ 3, α ∈ (0, N), λ 0 is a parameter and Iα is the Riesz potential. Under some appropriate assumptions on g, V(x) and f , we prove the existence of ground states and obtain the concentration behavior of the solutions when λ is large enough via variational methods.