Singular Dirichlet $(p,q)$-equations

We consider a nonlinear Dirichlet problem driven by the $(p,q)$-Laplacian and with a reaction having the combined effects of a singular term and of a parametric $(p-1)$-superlinear perturbation. We prove a bifurcation-type result describing the changes in the set of positive solutions as the parameter $\lambda >0$ varies. Moreover, we prove the existence of a minimal positive solution $u_{\lambda }^{\ast }$ and study the monotonicity and continuity properties of the map $\lambda \to u_{\lambda }^{\ast }$.