Abstract
In this paper, we study certain non-autonomous third order delay differential equations with continuous deviating argument and established sufficient conditions for the stability and boundedness of solutions of the equations. The conditions stated complement previously known results. Example is also given to illustrate the correctness and significance of the result obtained.
Highlights
This paper considers the third order non-autonomous nonlinear delay differential x′′′(t ) + a (t ) h ( x (t ), x′(t )) x′′(t ) + b (t ) g ( x′(t − r (t ))) + c (t ) f ( x (t − r (t ))) (1.1)= p (t, x (t ), x′(t ), x (t − r (t )), x′(t − r (t )), x′′(t ))or its equivalent systemHow to cite this paper: Olutimo, A.L. and Adams, D.O. (2016) On the Stability and Boundedness of Solutions of Certain Non-Autonomous Delay Differential Equation of Third Order
As in Theorem 1, the proof of Theorem 2 depends on the scalar differentiable Lyapunov function V
Example 3.1 We consider non-autonomous third-order delay differential equation x′′′(t )
Summary
This paper considers the third order non-autonomous nonlinear delay differential x′′′(t ) + a (t ) h ( x (t ), x′(t )) x′′(t ) + b (t ) g ( x′(t − r (t ))) + c (t ) f ( x (t − r (t ))) (1.1). (2016) On the Stability and Boundedness of Solutions of Certain Non-Autonomous Delay Differential Equation of Third Order. In a sequence of results, Omeike [11] considers the following nonlinear delay differential equation of the third order, with a constant deviating argument r, x′′′(t ) + a (t ) x′′(t ) + b (t ) g ( x′(t )) + c (t ) h ( x (t − r )) = p (t ). We establish sufficient conditions for the stability (when p ≡ 0 ) and boundedness (when p ≠ 0 ) of solutions of Equation (1.1) which extend and improve the results of Omeike [11] and Tunc [12]. The following will be our main stability result (when p ≡ 0 ) for (1.1)
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