On Asymptotics for Critical Solutions of Systems of Differential Equations with Oscillatory Decreasing Coefficients

P. N. Nesterov

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On Asymptotics for Critical Solutions of Systems of Differential Equations with Oscillatory Decreasing Coefficients

机译：具振荡递减系数的微分方程系统临界解的渐近性。

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摘要

In this paper we propose a method for constructing the asymptotics for a set of linear independent solutions of systems of differential equations with oscillatory decreasing coefficients. We illustrate this method by constructing the asymptotics for solutions of a system of two oscillators with slowly decreasing coupling and friction in one of the oscillators.

机译：在本文中，我们提出了一种构造具有渐减系数的微分方程组的线性独立解的渐近性的方法。我们通过构造渐近线来解决两个振荡器系统的解的渐近性，其中一个振荡器的耦合和摩擦逐渐减小。

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《Automatic Control and Computer Sciences》 |2013年第7期|共16页
作者
P. N. Nesterov;
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正文语种 eng
中图分类自动控制理论;
关键词
Oscillatory decreasing coefficients; Critical solutions; Method of averaging; Asymptotics; Coupled oscillators;

机译：振荡递减系数;临界解;平均法;渐近;耦合振子;

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专利

1. On Asymptotics for Critical Solutions of Systems of Differential Equations with Oscillatory Decreasing Coefficients [J] . P. N. Nesterov Automatic Control and Computer Sciences . 2013,第7期

机译：具振荡递减系数的微分方程系统临界解的渐近性。
2. Asymptotic integration of functional differential systems with oscillatory decreasing coefficients: a center manifold approach [J] . Nesterov Pavel Electronic Journal of Qualitative Theory of Differential Equations . 2016,第4期

机译：具有振荡递减系数的泛函系统的渐近积分：中心流形方法
3. Asymptotic integration of functional differential systems with oscillatory decreasing coefficients [J] . Pavel Nesterov Monatshefte für Mathematik . 2013,第2期

机译：具有振动递减系数的泛函微分系统的渐近积分。
4. Oscillatory Properties of First Order Neutral Delay Impulsive Differential Equations with Constant Coefficients [C] . M.B. Dimitrova, V.I. Donev International Conference on Application of Mathematics in Technical and Natural Sciences . 2009

机译：恒定系数第一订单中立延迟脉冲微分方程的振荡性质
5. On the Improved Asymptotics for Oscillatory Solutions of Second Order Ordinary Differential Equations. [D] . Heitman, Zhu Wang. 2014

机译：二阶常微分方程振动解的改进渐近性。
6. The Oscillation on Solutions of Some Classes of Linear Differential Equations with Meromorphic Coefficients of Finite p q-Order [O] . Hong-Yan Xu, Jin Tu, Zu-Xing Xuan 2013

机译：几类具有亚纯pq-阶亚纯系数的线性微分方程解的振动性
7. Center Manifold Method in the Asymptotic Integration Problem for Functional Differential Equations with Oscillatory Decreasing Coefficients. II [O] . P. N. Nesterov 2014

机译：具有振荡减小系数的功能微分方程的渐近积分问题中的中心歧管方法。 II
8. The asymptotic behavior of the solutions of differential equations containing large and rapidly changing coefficients [R] . Lyusternik, L. M., Vishik, M. I. 1967

机译：包含大且快速变化系数的微分方程解的渐近性态

On Asymptotics for Critical Solutions of Systems of Differential Equations with Oscillatory Decreasing Coefficients

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