We study the existence of positive solutions to the singular problem (eqution presented) where λ is a positive parameter, Δpu = div(Ι▽uΙp-2▽u), p > 1, Ω is a bounded domain in ℝn; n ≥ 1 with smooth boundary ∂ Ω, 0 < α < 1, and f : [0;∞) → ℝ is a continuous function which is asymptotically p-linear at 1. We prove the existence of positive solutions for a certain range of λ using the method of sub-supersolutions. We also extend our study to classes of systems which have forcing terms satisfying a combined asymptotically p-linear condition at ∞ and to corresponding problems on exterior domains.