On a class of singular p-Laplacian boundary value problems

We prove the existence and nonexistence of positive solutions for the boundary value problem { − Δ p u = λ f ( u ) in Ω , u = 0 on ∂ Ω , where Δ p u = div ( | ∇ u | p − 2 ∇ u ) , p > 1 , Ω is a bounded domain in R n with smooth boundary ∂Ω, f : ( 0 , ∞ ) → R is ( 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.