Existence of positive solutions for boundary value problem of second-order FDE

We use a fixed-point theorem in cones to investigate the existence of positive solutions for boundary value problem of a second-order Functional Differential Equation (FDE) with the form: y″(t) + r(t)ƒ(yt = 0, 0 < t 1, αy(t) − βy′(t) = ξ(t), −r ≤ t ≤ 0, γy(t) + δy′(t) =n(t), 1 ≤ t ≤ 1 + a, where yt(θ) = y(t + θ) for θ [−τ, a]. We allow that r(t) has the singularity at the endpoints t = 0 and t = 1 of [0, 1]. Our results include the situations that f is either superlinear or sublinear.