一类二阶微分方程解的稳定性和有界性

Q3 Mathematics

Differencialnie Uravnenia i Protsesy Upravlenia Pub Date : 2023-01-01 DOI:10.21638/11701/spbu35.2023.304

Adetunji Adedotun Adeyanju, Daniel Oluwasegun Adams

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引用次数: 0

摘要

本文利用Lyapunov的第二方法，研究了一类二阶微分方程的平凡解的一致渐近稳定性和所有解的最终有界性的充分条件。为了讨论前面提到的定性性质，我们构造了一个完备的李雅普诺夫函数。本文的有界性结果是新的，并且补充了文献中利用不完全Lyapunov函数和sgn函数得到的有界性结果。最后，我们用两个数值算例证明了我们的结果的正确性，并使用Maple软件对这些算例的解轨迹进行了图形化表示。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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On the Stability and Boundedness of Solutions to Certain Second Order Differential Equation

In this paper, we investigate by means of second method of Lyapunov, sufficient conditions that guarantee uniform-asymptotic stability of the trivial solution and ultimate boundedness of all solutions to a certain second order differential equation. We construct a complete Lyapunov function in order to discuss the qualitative properties mentioned earlier. The boundedness result in this paper is new and also complement some boundedness results in literature obtained by using an incomplete Lyapunov function together with a signum function. Finally, we demonstrate the correctness of our results with two numerical examples and graphical representation of the trajectories of solutions to the examples using Maple software.

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来源期刊

Differencialnie Uravnenia i Protsesy Upravlenia Mathematics-Analysis

CiteScore

1.10

自引率

0.00%

发文量