Existence of a positive solution for a p-Laplacian semipositone problem

We consider the boundary value problem −Δpu=λf(u) in Ω satisfying u=0 on ∂Ω, where u=0 on ∂Ω, λ>0 is a parameter, Ω is a bounded domain in â„Ân with C2 boundary ∂Ω, and Δpu:=div(|∇u|p−2∇u) for p>1. Here, f:[0,r]→℠is a C1 nondecreasing function for some r>0 satisfying f(0)