  We deal with existence and uniqueness of positive solutions of an elliptic
boundary value problem modeled by \begin{equation*} \begin{cases} \displaystyle
-\Delta_p u= \frac{f}{u^\gamma} + g u^q & \mbox{in $\Omega$,} \\ u = 0 &
\mbox{on $\partial\Omega$,} \end{cases} \end{equation*} where $\Omega$ is an
open bounded subset of $\mathbb{R}^N$, $\Delta_p u:=\text{div}(|\nabla
u|^{p-2}\nabla u)$ is the usual $p$-Laplacian operator, $\gamma\geq 0$ and
$0\leq q\leq p-1$; $f$ and $g$ are nonnegative functions belonging to suitable
Lebesgue spaces.
