On singular Sturm–Liouville boundary-value problems

We consider the existence of positive solutions for the boundary-value problem (q(t)ϕ(u′))′ + λ f(t,u) = 0, r 1, λ > 0, f is p -superlinear or p -sublinear at ∞ and is allowed to become −∞ at u = 0. Our results unify and extend many known results in the literature.