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In this paper, we consider the existence and concentration behavior of positive ground state solution to the following problem  −h p Δpu+V(x)|u| p−2 u = K(x)|u| q−2 u+ |u| p ∗ −2 u, x ∈ R N , u ∈W 1,p (R N ), u > 0, x ∈ R N , where h is a small positive parameter, 1 0, the equation has a positive ground state solution. Furthermore, we establish the concentration property of such solutions when h tends to zero.

Existence and concentration of ground state solution to a critical p-Laplacian equation