Positive Solutions for Higher Order Ordinary Differential Equations

Abstract

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