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In this paper, we mainly consider the asymptotic behaviors of positive weak solutions to the following critical quasilinear elliptic equation with Hardy potential −div|∇u|p−2∇u |x| ap − γ u p−1 |x| (a+1)p = u p∗ a,b−1 |x| bp∗ a,b , x ∈ RN , where 1 < p < N, 0 ≤ a < N−p p , a ≤ b < a + 1, 0 ≤ γ < N−(a+1)p p p and p∗ a,b = N p N−(a+1−b)p . The main results of this paper generalize the some related works of [8, 23].
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