Arbitrary many peak solutions for a bi-harmonic equation with nearly critical growth

Let Ω be the unit ball centered at the origin in R N ( N > 6 ) . In this paper we study the following problem { Δ 2 u = | x | τ u p − ε , x ∈ Ω u > 0 , x ∈ Ω u = 0 , Δ u = 0 , x ∈ ∂ Ω where p = N + 4 N − 4 , τ > 0 , ε > 0 . We prove that for any k ∈ N + , if ε is small enough, the above problem has a positive solution u ε concentrating at k distinct points tending to the boundary of Ω as ε goes to 0 + .