Concentration of ground states for a quasilinear Schrödinger equation with a parameter

In this paper, we study the existence and concentration behavior of positive solutions for a quasilinear Schrödinger equations of the form −ε2Δu+V(x)u−ε2Δ(|u|2α)|u|2α−2u=g(u)in RN, where α>12 is a parameter and N≥3. Under some appropriate assumptions on the potential V, we prove the existence of positive ground state solutions which concentrate at a local minimum point of V as ε→0+.