In this paper we study the following eigenvalue problem {-Delta v = lambda C(alpha)(p(alpha) - epsilon)vertical bar x vertical bar(alpha)u(epsilon)(p alpha-epsilon-1)v in Omega, u=0 on partial derivative Omega, where Omega subset of R-N is a smooth bounded domain containing the origin, C(alpha) = (N + alpha)(N - 2), N >= 3, p(alpha) = N+2+2 alpha/N-2, alpha > 0, epsilon > 0 is a small parameter and u(epsilon) is a single peaked solution of Henon equation {-Delta u = C(alpha)vertical bar x vertical bar(alpha)u(p alpha-epsilon) in Omega, u > 0 in Omega, u=0 on partial derivative Omega, which est...