Double-spike solutions for a critical inhomogeneous elliptic problem in domains with small holes

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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⊂ℝNis 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.
Original languageEnglish
Pages (from-to)671-692
Number of pages22
JournalProceedings of the Royal Society of Edinburgh Section A: Mathematics
DOIs
Publication statusPublished - 1 Aug 2008
Externally publishedYes

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