Positive solutions for slightly super-critical elliptic equations in contractible domains

We give examples of bounded domains Omega, even contractible, having the following property: there exists (k) over bar(Omega) such that, for every integer k greater than or equal to (k) over bar(Omega), problem P(epsilon, Omega) below, for epsilon > 0 small enough, has at least one solution blowing up as epsilon --> 0 at exactly k points. We also prove that the blow-up points tend to some points of partial derivativeOmega as k --> infinity. (C) 2002 Academie des science/Editions scientifiques et medicales Elsevier SAS.