Quasilinear elliptic equations with singular quadratic growth terms

In this paper we deal with positive solutions for singular quasilinear problems whose model is $$ \begin{cases} -Δu + \frac{|\nabla u|^2}{(1-u)^γ}=g & \mbox{in $Ω$,}\newline \hfill u=0 \hfill & \mbox{on $\partialΩ$,} \end{cases} $$ where $Ω$ is a bounded open set of $\mathbb{R}^N$, $g\geq 0 $ is a function in some Lebesgue space, and $γ>0$. We prove both existence and nonexistence of solutions depending on the value of $γ$ and on the size of $g$.