Positive solutions of a nonlinear m-point boundary value problem

Let ai ≥ 0 for i = 1,…, m − 3 and am−2 > 0. Let ξi satisfy 0 < ξ1 < ξ2 < … < ξm−2 < 1 and Σm−2i=1 aiξi < 1. We study the existence of positive solutions to the boundary-value problem where a ε C([0, 1], [0, ∞)), and f ε C([0, ∞), [0, ∞)). We show the existence of at least one positive solution if f is either superlinear or sublinear by applying a fixed-point theorem in cones.