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

Let ΩΩ be the unit ball centered at the origin in RN(N>6)RN(N>6). In this paper we study the following problem {Δ2u=|x|τup−ε,x∈Ωu>0,x∈Ωu=0,Δu=0,x∈∂Ω where p=N+4N−4, τ>0,ε>0τ>0,ε>0. We prove that for any k∈N+k∈N+, if εε is small enough, the above problem has a positive solution uεuε concentrating at kk distinct points tending to the boundary of ΩΩ as εε goes to 0+0+.