  In this paper we consider a Dirichlet problem driven by an anisotropic
$(p,q)$-differential operator and a parametric reaction having the competing
effects of a singular term and of a superlinear perturbation. We prove a
bifurcation-type theorem describing the changes in the set of positive
solutions as the parameter moves. Moreover, we prove the existence of a minimal
positive solution and determine the monotonicity and continuity properties of
the minimal solution map.
