New type of solutions to a slightly subcritical Hénon type problem in dimensions 7, 8 and 9

Abstract

Inspired from the constructive method of Davilla et al. [10], with new ingredients, we extend their existence results to dimensions 7≤n≤9 concerning the following Hénon type problem{−Δu=K|u|p−1−εuinΩ,u=0on∂Ω, where Ω is a smooth bounded domain in Rn, ε is a positive real parameter, p+1=2n/(n−2) is the critical Sobolev exponent and the function K∈C2(Ω‾) is positive satisfying condition (1.1).