  We consider a nonlinear Dirichlet problem driven by the $(p,q)$-Laplacian
with $1<q<p$. The reaction is parametric and exhibits the competing effects of
a singular term and of concave and convex nonlinearities. We are looking for
positive solutions and prove a bifurcation-type theorem describing in a precise
way the set of positive solutions as the parameter varies. Moreover, we show
the existence of a minimal positive solution and we study it as a function of
the parameter.
