Bubble towers for supercritical semilinear elliptic equations

We construct positive solutions of the semilinear elliptic problem u + u + up = 0 with Dirichet boundary conditions, in a bounded smooth domain ⊂ RN (N 4), when the exponent p is supercritical and close enough to N+2 N−2 and the parameter ∈ 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 is a ball and the solutions are radially symmetric. © 2004 Elsevier Inc. All rights reserved.