LINEAR PERTURBATIONS FOR THE CRITICAL HENON PROBLEM

In this paper, we study the problem { -Delta u = vertical bar x vertical bar(alpha)u(p alpha) + is an element of vertical bar x vertical bar(beta)u in Omega u > 0 in Omega u = 0 on partial derivative Omega where p alpha = N+2+2 alpha/N-2 Omega is a smooth bounded domain of R-N with 0 is an element of Omega and N >= 4. We show that, for alpha >= 0 and 0 <= beta <= N - 4, there exists one solution concentrating at x = 0 as is an element of 0. Moreover, we prove that, if Omega is a ball, there exist no radial solution if alpha = beta > N - 4.