We study positive solutions to the singular boundary value problem    −∆ p u = λ f (u) u β in Ω u = 0 on ∂Ω, where ∆ p u = div (|∇u| p−2 ∇u), p > 1, λ > 0, β ∈ (0, 1) and Ω is a bounded domain in R N , N ≥ 1. Here f : [0, ∞) → (0, ∞) is a continuous nondecreasing function such that lim u→∞ f (u) u β+p−1 = 0. We establish the existence of multiple positive solutions for certain range of λ when f satisfies certain additional assumptions. A simple model that will satisfy our hypotheses is f (u) = e αu α+u for α ≫ 1. We also extend our results to classes of systems when the nonlinearities satisfy a combined sublinear condition at infinity. We prove our results by the method of sub-supersolutions.

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