We study the existence of positive solutions of the differential equation (−1)my(2m) (t) = f(t, y(t), y″(t),…, y(2(m−1)) (t)) with the boundary condition y(2i)(0) = 0 = y(2i)(1), 0 ≤ i ≤ m − 1, and y(2i)(0) = 0 = y(2i+1)(1), 0 ≤ i ≤ m − 1. We show the existence of at least one positive solution if f is either superlinear or sublinear by an application of a fixed-point theorem in a cone.
