On the Asymptotic Stability of Solutions for a Certain Non-autonomous Third-order Delay Differential Equation

In this paper, we shall establish sufficient conditions for the asymptotic stability of the zero solution for a certain nonlinear non-autonomous third-order delay differential equation of the following type

+ a(t)ẍ + b(t)g(ẋ (t − r(t))) + c(t)h(x(t − r(t))) = 0.

By using a Lyapunov functional as a basic technique, we obtain a result which includes and improves some related results in literature. An example is given in the last section of this paper, to illustrate our main result of stability.