Application of Lyapunov's Direct Method to the Study of the Stability of Solutions to Systems of Impulsive Differential Equations

A. I. Dvirnyi; V. I. Slynko

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Application of Lyapunov's Direct Method to the Study of the Stability of Solutions to Systems of Impulsive Differential Equations

机译：李雅普诺夫直接法在脉冲微分方程组解稳定性研究中的应用

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Classical theorems on the stability of the solutions of impulsive differential equations are further developed.

机译：进一步发展了关于脉冲微分方程解稳定性的经典定理。

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《Mathematical notes》 |2014年第2期|26-37|共12页
作者
A. I. Dvirnyi; V. I. Slynko;
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作者单位

Hedmark University College, Hedmark, Norway Timoshenko Institute of Mechanics, National Academy of Sciences, Kiev, Ukraine;

Hedmark University College, Hedmark, Norway Timoshenko Institute of Mechanics, National Academy of Sciences, Kiev, Ukraine;

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正文语种 eng
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关键词
impulsive differential equation; Lyapunov's direct method; Lyapunov (asymptotic) stability; Cauchy problem; equilibrium state stability; Hahn function class;

机译：脉冲微分方程李雅普诺夫的直接方法;Lyapunov（渐近）稳定性;柯西问题;平衡态稳定性哈恩函数类;

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1. Stability of the zero solution of impulsive differential equations by the Lyapunov second method [J] . Akhmetov MU., Zafer A. Journal of Mathematical Analysis and Applications . 2000,第1期

机译：Lyapunov第二方法求解脉冲微分方程零解的稳定性
2. Second method of Lyapunov for stability of linear impulsive differential-difference equations with variable impulsive perturbations [J] . D. D.Bainov, I. M.Stamova, A. S.Vatsala International journal of stochastic analysis . 1998,第2期

机译：具有可变脉冲摄动的线性脉冲微分方程稳定性的Lyapunov第二种方法
3. On Lyapunov stability of a class of linear systems of generalized ordinary differential equations and linear impulsive systems [J] . M. Ashordia Memoirs on Differential Equations and Mathematical Physics . 2004,第1期

机译：一类广义常微分方程线性系统和线性脉冲系统的Lyapunov稳定性
4. On a New Method for Studying Stability in the Whole by a Part of the Variables of Solutions of Systems of Ordinary Differential Equations [C] . M.Yu. Filimonov International Conference "Applications of Mathematics in Engineering and Economics" . 2016

机译：以常微分方程系统解决方案的一部分研究整体稳定性的新方法
5. A study of the existence of solutions to some inital value problems for impulsive differential equations. [D] . Brennan, Michael. 1995

机译：研究脉冲微分方程某些初值问题解的存在性。
6. A Study of Impulsive Multiterm Fractional Differential Equations with Single and Multiple Base Points and Applications [O] . Yuji Liu, Bashir Ahmad -1

机译：具有单基点和多基点的脉冲多项式分数阶微分方程的研究及其应用
7. Stability of the Zero Solution of Impulsive Differential Equations by the Lyapunov Second Method [O] . Akhmetov M.U., Zafer A. 2000

机译：Lyapunov第二法确定脉冲微分方程零解的稳定性
8. Lyapunov stability for partial differential equations. Part 1 - Lyapunov stability theory and the stability of solutions to partial differential equations. Part 2 - Contraction groups and equivalent norms [R] . Buis, G. R., Eisen, M. M., Vogt, W. G. 1968

机译：偏微分方程的Lyapunov稳定性。第1部分 - Lyapunov稳定性理论和偏微分方程解的稳定性。第2部分 - 收缩组和等效规范

Application of Lyapunov's Direct Method to the Study of the Stability of Solutions to Systems of Impulsive Differential Equations

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