Existence and concentration of ground state solutions for a subcubic quasilinear problem via Pohozaev manifold

In this paper, we study the following quasilinear Schrödinger equation−ε2Δu+V(x)u−ε212Δ(u2)u=K(x)|u|p−1u, where 10ε>0 is a small parameter, and V(x)V(x) has global minimum and K(x)K(x) has global maximum. We show the existence of ground state for ε>0ε>0 via a constrained minimization on Pohozaev manifold. Furthermore, we prove these ground state solutions concentrate at some set related to the linear potential V(x)V(x) and the nonlinear potential K(x)K(x).