On the profile of sign-changing solutions of an almost critical problem in the ball

We study the existence and the profile of sign-changing solutions to the slightly subcritical problem -Delta u - vertical bar u vertical bar(2*-2-epsilon)u in B, u - 0 on partial derivative B, where B is the unit ball in R-N, N >= 3, 2* = 2N/(N - 2) and epsilon > 0 is a small parameter. Using a Lyapunov-Schmidt reduction, we discover two new nonradial solutions having three bubbles with different nodal structures. An interesting feature is that the solutions are obtained as a local minimum and a local saddle point of a reduced function, hence they do not have a global min-max description.