Multi-Peak Solutions for Super-Critical Elliptic Problems in Domains with Small Holes

AbstractThis paper deals with the slightly super-critical elliptic problem−Δu=u(N+2)/(N−2)+εin Ωu>0in Ωu=0on ∂Ω, (1) where ε>0 is a small parameter and Ω ⊂RN is a bounded domain with smooth boundary. Assuming that the domain exhibits k sufficiently small holes, multiple solutions are constructed by gluing double-spike patterns located near each of the holes