Existence of positive periodic solutions for higher-order ordinary differential equations

AbstractThis paper deals with the existence of positive periodic solutions for the nth-order ordinary differential equation u(n)(t)=f(t,u(t),u′(t),…,u(n−1)(t)), where n≥2, f:R×[0,∞)×Rn−1→R is a continuous function and f(t,x0,x1,…,xn−1) is 2π-periodic in t. Some existence results of positive 2π-periodic solutions are obtained assuming f satisfies some superlinear or sublinear growth conditions on x0,x1,…,xn−1. The discussion is based on the fixed point index theory in cones