#### Event Details

For a bounded domain $\Omega$, a bounded Carathéodory function $g$ in $\Omega\times\mathbb{R}$,
$p>1$ and a nonnegative measurable function $h$ in $\Omega$ which is strictly positive in a set of positive measure we prove that, contrarily with the case $h\equiv 0$, there exists a solution of the semilinear elliptic problem
$$
\left \{
\begin{array}{rcll}
-\Delta u & = & \lambda u +g(x,u)- h |u|^{p-1} u +f, & \mbox{in } \Omega \\
u & = & 0, & \mbox{on } \partial\Omega,\\
\end{array}
\right.
$$
for every
$\lambda\in \mathbb{R}$ and
$f\in\ L^2(\Omega)$.