Positive solutions of higher-order periodic boundary value problems

This paper deals with the existence of positive solutions for nth-order periodic boundary value problem where Ln u(t) = u(n)(t) + Σi=0n−1 ai u(i)(t) is an nth-order linear differential operator and ƒ :[0, 2π] × + → + is continuous. We obtain a sufficient condition that operator La satisfies the maximum principle in periodic boundary condition. Using this maximum principle and fixed-point index theory in cones, we obtain existence results of positive solutions.