Sign-changing blowing-up solutions for the Brezis-Nirenberg problem in dimensions four and five

We consider the Brezis-Nirenberg problem -Delta u = lambda u + vertical bar u vertical bar(p-1) u in Omega, u = 0 on partial derivative Omega, where Omega is a smooth bounded domain in R-N, N >= 3, p = N+2/N-2 and lambda > 0. We prove that, if Omega is symmetric and N = 4, 5, there exists a sign-changing solution whose positive part concentrates and blowsup at the center of symmetry of the domain, while the negative part vanishes, as lambda -> lambda(1), where lambda(1) = lambda(1)( Omega) denotes the first eigenvalue of -Delta on Omega, with zero Dirichlet boundary condition.