On the Existence of Periodic Solutions To Nonlinear Third Order Ordinary Differential Equations With Delay

Abstract

In this paper, we are concerned with the existence of periodic Solutions to nonlinear third order delay differential equation: x'''(t) + psi(x'(t))x('')(t) + g(x'(t - r)) + f(x(t)) = p(t, x(t), x(t - r), x'(t), x'(t - r), x ''(t)), when p(t, x(t), x(t - r), x'(t), x'(t - r), x ''(t)) is a periodic function of period T, T > 0. With use of Lyapunov's functional approach, we establish some new sufficient conditions which guarantee that there exists a periodic solution of this equation of period T, T > 0. For illustrations, an example is also given on the existence of periodic solutions.