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