Bubble towers for supercritical semilinear elliptic equations

We construct positive solutions of the semilinear elliptic problem Δu + λu + u^p = 0 with Dirichet boundary conditions, in a bounded smooth domain Ω ⊂ ℝ^N (N ≥ 4), when the exponent p is supercritical and close enough to N+2/N-2 and the parameter λ ∈ 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 Ω is a ball and the solutions are radially symmetric.