On Dirichlet problems with singular nonlinearity of indefinite sign

Abstract Let Ω be a smooth bounded domain in R N , 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 − Δ u = K ( x ) u − α − λ M ( 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 − Δ u = m ( x ) u − γ in Ω, u = 0 on ∂Ω, where m is allowed to change sign in Ω.