We consider the boundary value problem − Δ p u = λ f ( u ) in Ω satisfying u = 0 on ∂ Ω , where u = 0 on ∂ Ω , 0$"> λ > 0 is a parameter, Ω is a bounded domain in ℝ n with C 2 boundary ∂ Ω , and Δ p u : = div ( | ∇ u | p − 2 ∇ u ) for 1$"> p > 1 . Here, f : [ 0 , r ] → ℝ is a C 1 nondecreasing function for some 0$"> r > 0 satisfying f ( 0 ) < 0 (semipositone). We establish a range of λ for which the above problem has a positive solution when f satisfies certain additional conditions. We employ the method of subsuper solutions to obtain the result.