Bubble towers for supercritical semilinear elliptic equations

We construct positive solutions of the semilinear elliptic problem Delta u+ lambda u + u(P) = 0 with Dirichet boundary conditions, in a bounded smooth domain Omega subset of R-N (N >= 4), when the exponent p is supercritical and close enough to N+2/N-2 and the parameter lambda is an element of R is small enough. As p -> N+2/N-2, the solutions have multiple blow up at finitely many points which are the critical points of a function whose definition involves Green's function. Our result extends the result of Del Pino et al. (J. Differential Equations 193(2) (2003) 280) when Omega is a ball and the solutions are radially symmetric. (c) 2004 Elsevier Inc. All rights reserved.