Positive Periodic Solutions of Third-Order Ordinary Differential Equations with Delays.

The existence results of positive ω-periodic solutions are obtained for the third-order ordinary differential equation with delays u'"(t)+a(t)u(t) = f(t,u(t-τ0), u'(t-τ1), u"(t-τ2)), t ∈ ℝ, where a ∈ C(R,(0, ∞)) is ω-periodic function and f: ℝ x[0, ∞) x ℝ² → (0, ∞) is a continuous function which is ω-periodic in t, and τ0, τ1, τ2 are positive constants. The discussion is based on the fixed- point index theory in cones. [ABSTRACT FROM AUTHOR]