Infinitely many double-boundary-peak solutions for a Hénon-like equation with critical nonlinearity

In this paper we study the following Hénon-like equation{−Δu=||y|−2|αup,u>0,inΩ,u=0,on∂Ω, where α>0α>0, p=N+2N−2, Ω={y∈RN:1<|y|<3}Ω={y∈RN:1<|y|<3}, N≥4N≥4. We show that for α>0α>0 the above problem has infinitely many positive solutions concentrating simultaneously near the interior boundary {x∈RN:|x|=1}{x∈RN:|x|=1} and the outward boundary {x∈RN:|x|=3}{x∈RN:|x|=3}, whose energy can be made arbitrarily large.