In this paper we deal with the existence of positive solutions for the following nonlocal type of problems
$$\everymath{\displaystyle} \left\{ \begin{array}{l@{\quad}l} -\Delta u = \frac{\sigma}{( \int_{\varOmega} g(u)\, dx )^p} f(u) & \mbox{in}\ \varOmega, \\[3mm] u>0 & \mbox{in}\ \varOmega, \\[1mm] u=0 & \mbox{on}\ \partial\varOmega, \end{array} \right. $$
where *Ω* is a bounded smooth domain in ℝ^{N} (*N*≥1), *f*,*g* are continuous positive functions, *σ*>0 and *p*∈ℝ.

We give sufficient conditions on the functions *f* and *g* in order to have existence of positive solutions.