Positive periodic solutions of first and second order ordinary differential equations

In this paper the existence results of positive omega-periodic solutions are obtained for second order ordinary differential equation -u"(t) = f (t, u(t)) (t is an element of R), and also for first order ordinary differential equation u'(t) = f (t, u(t)) (t is an element of R), where f : R x R+ --> R is a continuous function which is omega-periodic in t. The discussion is based on the fixed point index theory in cones.