Positive solutions for higher order ordinary differential equations.

Solutions that are positive with respect to a cone are obtained for the boundary value problem, u(n) + a(t)f(u) = 0, u(i)(0) = u(n−2)(1) = 0, 0 ≤ i ≤ n − 2, in the cases that f is either superlinear or sublinear. The methods involve application of a fixed point theorem for operators on a cone.