Existence of two solutions for the Bahri–Coron problem in an annular domain with a thin hole

We will show that the problem − u = |u|4/(N−2)u in Ω, u =0 on∂Ω has at least two pairs of solutions if Ω is an annular domain with a thin hole in RN (N 3). © 2011 Elsevier Inc. All rights reserved.