On a class of singular p-Laplacian boundary value problems

We prove the existence and nonexistence of positive solutions for the boundary value problem{−Δpu=λf(u)in Ω,u=0on ∂Ω, where Δpu=div(|∇u|p−2∇u)Δpu=div(|∇u|p−2∇u), p>1p>1, Ω   is a bounded domain in RnRn with smooth boundary ∂Ω  , f:(0,∞)→Rf:(0,∞)→R is (p−1)(p−1)-subhomogeneous at ∞ and is allowed to change sign, and λ is a large parameter. Our approach is based on the method of sub- and supersolutions.