Abstract

Let D be a bounded, smooth domain in RN, N ≥ 3, P ∈ D. We consider the boundary value problem in Ω = D {set minus} Bδ (P),Δ u + up = 0, u > 0 in  Ω, u = 0 on  ∂ Ω, with p supercritical, namely p > frac(N + 2, N - 2). We find a sequencep1 < p2 < p3 < ⋯, with  under(lim, k → + ∞) pk = + ∞, such that if p is given, with p ≠ pj for all j, then for all δ > 0 sufficiently small, this problem is solvable. © 2006 Elsevier Masson SAS. All rights reserved.