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

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