Existence of positive solutions for the Hénon equation involving critical Sobolev terms

Abstract

Let N ≥ 3, 2* = 2 N / (N - 2) and Ω ⊂ RN be a bounded domain with a smooth boundary ∂Ω and 0 ∈ Ω. Our purpose in this paper is to consider the existence of solutions of Hénon equation:{(- Δ u (x) = | x |α | u (x) |2* - 1, in Ω,; u > 0, in Ω,; u = 0, on ∂ Ω,) where α > 0. © 2009 Elsevier Inc. All rights reserved.