In this paper, we study the existence of positive solutions for the quasilinear elliptic singular problem
$$\left\{\begin{array}{ll}-\Delta u + c\,\frac{|\nabla u|^2}{u^\gamma} = \lambda\,f(u), \quad \quad \mbox{in $\Omega$},\\ u=0, \quad \qquad \qquad \qquad \quad \, \, \, \, \, \mbox{on $\partial$$\Omega$},\end{array}\right.$$
where
\({c,\lambda >0}\),
\({\gamma \in (0,1)}\),
f is strictly increasing and derivable in
\({0,\infty)}\) with
\({f(0)>0}\). We show that there exists
\({\lambda^*>0}\) such that
\({(0,\lambda^*]}\) is the maximal set of values such there exists solution. In addition, we prove that for
\({\lambda<\lambda^*}\) there exists minimal and bounded solutions. Moreover, we give sufficient conditions for existence and regularity of solutions for
\({\lambda=\lambda^*}\).