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 -\De u=|u|^{2^*-2-\eps}u \hbox{in} \cB, \quad u=0 \hbox{on}\partial \cB, where \cB is the unit ball in \rr^N, $N\geq 3$, $2^*=\frac{2N}{N-2}$ and \eps>0 is a small parameter. Using a Lyapunov-Schmidt reduction we discover two new non-radial solutions having 3 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.Comment: 3 figure