Existence and concentration of ground state solutions for critical Kirchhoff-type equation with steep potential well

Abstract

In this paper, we study the nonlinear Kirchhoff type equation where a, b are positive constants and . Suppose that the nonnegative continuous potential V represents a potential well with the bottom and satisfies certain assumptions. We obtain the existence of ground state solutions by using the variational methods. Moreover, the concentration behavior of the ground state solutions as is also worth considering.