On Dirichlet problems with singular nonlinearity of indefinite sign

Let Ω be a smooth bounded domain in RN, N≥1, let K, M be two nonnegative functions and let α,γ>0. We study existence and nonexistence of positive solutions for singular problems of the form −Δu=K(x)u−α−λM(x)u−γ in Ω, u=0 on ∂Ω, where λ>0 is a real parameter. We mention that as a particular case our results apply to problems of the form −Δu=m(x)u−γ in Ω, u=0 on ∂Ω, where m is allowed to change sign in Ω.