Existence of ground state solutions for critical quasilinear Schrödinger equations with steep potential well

Abstract

Abstract We study the existence of solutions for the quasilinear Schrödinger equation with the critical exponent and steep potential well. By using a change of variables, the quasilinear equations are reduced to a semilinear one, whose associated functionals satisfy the geometric conditions of the Mountain Pass Theorem for suitable assumptions. The existence of a ground state solution is obtained, and its concentration behavior is also considered.