On the existence and the profile of nodal solutions of elliptic equations involving critical growth

We study the existence of sign changing solutions to the slightly subcritical problem -Delta u = \u\(p-1-epsilon) 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 epsilon > 0. We prove that, for e small enough, there exist N pairs of solutions which change sign exactly once. Moreover, the nodal surface of these solutions intersects the boundary of Omega, provided some suitable conditions are satisfied.