Nonlinear elliptic equations with critical Sobolev exponent in nearly starshaped domains

Under suitable assumptions on Omega, we show that, for epsilon > 0 small and k large enough, problem (1) below has solutions which concentrate and blow-up as epsilon --> 0 at exactly k points; the blowing-up points approach partial derivativeOhm as k --> infinity; the number of solutions tends to infinity as epsilon --> 0. These assumptions allow Ohm to be contractible and even arbitrarily close to starshaped domains. (C) 2002 Academie des sciences/Editions scientifiques et medicales Elsevier SAS.