| Contents |
| We consider the semilinear Lane-Emden problem
\begin{equation}\label{problemAbstract}\left\{\begin{array}{lr}-\Delta u= |u|^{p-1}u\ & \ \mbox{ in }\Omega\\
u=0\ & \ \mbox{ on }\partial \Omega
\end{array}\right.\tag{$\mathcal E_p$}
\end{equation}
where $p>1$ and $\Omega$ is a smooth bounded simply connected domain of $\mathbb R^2$.
By imposing some symmetry on the domain we show the existence, for $p$ sufficiently large, of sign-changing solutions $u_p$ having two nodal regions and whose nodal line doesn't touch the boundary.
The results presented are obtained in collaboration with F. De Marchis (Universita Tor Vergata, Roma) and F. Pacella (Universita Sapienza, Roma). |
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