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

Abstract EN

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 - τ 0 ) , u ′ ( t - τ 1 ) , u ′′ ( t - τ 2 ) ) , t ∈ ℝ, where a ∈ C ( ℝ , ( 0 , ∞ ) ) is ω -periodic function and f : ℝ × [ 0 , ∞ ) × ℝ 2 → [ 0 , ∞ ) is a continuous function which is ω -periodic in t , and τ 0 , τ 1 , τ 2 are positive constants.

The discussion is based on the fixed-point index theory in cones.