... ≤maxΩ u f (x,t), so ∃λ0 > such that u is a supersolution of (1.1) ∀λ ∈ (0,λ0 ) by (1.2) (3.5) 380 Positive solutions of singular p-Laplacian problems Let a(x)u(x)−γ + λ f x,u(x) , t > u(x) ... is a subsolution of (1.1) ∀λ ∈ (0,λ0 ) The rest of the proof now proceeds as above Proofs of Theorems 1.4 and 1.5 Proof of Theorem 1.4 Define a Carath´ odory function on Ω × R by e a(x)t −γ ... Swanson, Entire positive solutions of singular semilinear elliptic equations, Japan J Math (N.S.) 11 (1985), no 1, 145–155 A V Lair and A W Shaker, Classical and weak solutions of a singular semilinear...