Abstract

In this paper we construct solutions which develop two negative spikes as ε→0+ for the problem Δu=|u| 4/(N-2)u+εf(x) in Ω, u=0 on ∂Ω, where Ω⊂ℝN is a bounded smooth domain exhibiting a small hole, with f≥0, f≠0. This result extends a recent work of Clapp et al. in the sense that no symmetry assumptions on the domain are required. © 2008 The Royal Society of Edinburgh.