In this paper we consider the existence of positive solutions for
the following class of singular elliptic nonlocal problems of
Kirchhoff-type
$$
\left\{\begin{array}{rclcc}
-M(\|u\|^{2})\Delta u = \frac{h(x)}{u^{\gamma}}+k(x)u^{\alpha} \mbox{in} \Omega ,\\
u > 0 \mbox{in} \Omega ,\\
u = 0 \mbox{on} \partial\Omega ,\\
\end{array}
\right.
$$
where $\Omega \subset \mathbb R^{N}, N \geq 2,$ is a bounded smooth
domain, $M:\mathbb{R}\rightarrow \mathbb{R}$ is a continuous
function and $\|u\|^{2}=\int_{\Omega}|\nabla u|^{2}$ is the usual
norm in $H^{1}_{0}(\Omega )$. The main tools used are the Galerkin
method and a Hardy-Sobolev inequality.