Lyapunov Functions in Justification Theorems for Asymptotics

被引：5
|
作者：
Kalyakin, L. A. [1 ]
机构：
[1] Russian Acad Sci, Ctr Comp, Inst Math, Ufa Sci Ctr, Ufa 450001, Russia
来源：
MATHEMATICAL NOTES | 2015年 / 98卷 / 5-6期
基金：
俄罗斯科学基金会;
关键词：
ordinary differential equations; asymptotic solution; singular point; exact solution; Lyapunov function; dynamical system; AUTORESONANCE MODELS; SYSTEM;
D O I：
10.1134/S000143461511005X
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
A formal asymptotic solution is considered for a nonlinear system of ordinary differential equations in a neighborhood of a singular point. The problem of existence of an exact solution with such an asymptotics and the problem of stability of this solution are solved. The main tool in these studies is the Lyapunov function for a system linearized on a formal solution.
引用
收藏
页码：752 / 764
页数：13
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