Concentrating boundary blow up solutions of a slightly subcritical Hénon type problem for all dimensions

In this paper, we extend the result of Davila et al. [7] by constructing some concentrating boundary blow up solutions of the subcritical exponent PDE. (Pε): −Δu=K|u|4/(n−2)−εu in Ω, u=0 on ∂Ω, with ε>0 and n≥3. The new idea is to change the bubble Pδa,λ used in [7] by another approximate solution Pδ˜a,λ (see Section 4) to improve the estimate of some integrals which contain a remainder function v.