POSITIVE PERIODIC SOLUTIONS OF FIRST AND SECOND ORDER ORDINARY DIFFERENTIAL EQUATIONS

Abstract

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