Positive solutions of an m-point boundary value problem with sign changing nonlinearities

Let ai > 0 for i = 1, …, m − 2. Let ξi satisfy 0 = ξ0 < ξ1 < ξ2 < … < ξm−2 < ξm−1 = 1 and ∑m−2i=1 aiξi < 1. We study the existence of positive solutions to the boundary value problem where f is allowed to change sign. We provide sufficient conditions for the existence of at least two positive solutions by applying a new fixed-point theorem in cones.