Supercritical elliptic problems in domains with small holes

Abstract

Let D be a bounded, smooth domain in R-N, N >= 3, P is an element of D. We consider the boundary value problem in Omega = D \ B delta (P), Delta u +u(p) =0, u > 0 i n Omega, u = 0 on partial derivative Omega, with p supercritical, namely p > N+2/N-2 We find a sequence (GRAPHICS) such that if p is given, with p not equal p(j) for all j, then for all delta > 0 sufficiently small, this problem is solvable. (C) 2006 Elsevier Masson SAS. All rights reserved.