  We deal with existence, uniqueness and regularity of nonnegative solutions to
a Dirichlet problem for equations as \begin{equation*} \displaystyle
-\operatorname{div}\left(\frac{|\nabla u|^{p-2}\nabla
u}{(1+u)^{\theta(p-1)}}\right) = h(u)f \quad \text{in }\Omega, \end{equation*}
where $\Omega$ is an open bounded subset of $\mathbb{R}^N$ ($N\ge 2$), $p>1$,
$\theta\ge 0$, $f\geq 0$ belongs to a suitable Lebesgue space and $h$ is a
continuous, nonnegative function which may blow up at zero and it is bounded at
infinity.
