Existence and nonexistence of positive solutions for singular (p,q)-equations with superdiffusive perturbation

We consider a nonlinear Dirichlet problem driven by the $(p,q)$-Laplacian and with a reaction which is parametric and exhibits the combined effects of a singular term and of a superdiffusive one. We prove an existence and nonexistence result for positive solutions depending on the value of the parameter $lambda in overset{circ}{mathbb{R}}_+=(0,+infty)$.