In this paper, we consider the problem f q−1 (x) = Ω |x| α |y| β f (y) |x − y| n−γ dy, f > 0, x ∈ Ω, where Ω is the unit ball in R n (n ≥ 3) centered at the origin, 1 < γ < n and α, β > 0, qγ := 2n n+γ < q < 2. We will investigate the asymptotic behavior of energy maximizing positive solution as q → (2n n+γ) + = (qγ) +. We also show that the energy maximizing positive solution concentrate at a point, which is located at the boundary as q → (qγ) +. In addition, the energy maximizing positive solution is non-radial provided that q closes to qγ .

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