Ricerc@Sapienza

We study weak solutions of the problem
$$
\begin{dcases*}
\ - \Delta u = \frac{\lambda}{|x|^2} u + u^p & \ \ \ in \ $\Omega \backslash\{0\}$\\
\ u \geq 0 & \ \ \ in \ $\Omega \backslash\{0\}$\\
\ u|_{\partial \Omega} =0 &
\end{dcases*}
$$
where $\Omega \subseteq \real^N$ is a smooth bounded domain containing the origin, $N \geq 3$, $1