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

Abstract

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 $\rr^N$, $N\ge 3$, $2^{\ast }=\frac{2N}{N-2}$ 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.

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Cited by in corpus (2)

• Sharp concentration estimates near criticality for radial sign-changing solutions of Dirichlet and Neumann problems
• Nodal bubble tower solutions to slightly subcritical elliptic problems with Hardy terms