Lyapunov-Razumikhin pairs in the instability problem for infinite delay equations

被引：1
|
作者：
Sedova, N. O. [1 ]
机构：
[1] Ulyanovsk State Univ, Dept Math & Informat Technol, Ulyanovsk 432000, Russia
来源：
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2010年 / 73卷 / 07期
基金：
俄罗斯基础研究基金会;
关键词：
Delay differential equation; Infinite delay; Instability; Lyapunov-Razumikhin pairs; Limiting equations; FUNCTIONAL-DIFFERENTIAL EQUATIONS;
D O I：
10.1016/j.na.2010.06.027
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Some theorems on complete instability of the zero solution relative to a set for nonautonomous nonlinear equations with infinite delay are provided. The right-hand side of the equation is assumed to be defined in a fading memory space and to satisfy conditions that allow the construction of limiting equations. We use conceptions of Lyapunov-Razumikhin pairs and limiting equations to obtain new instability results, which are applicable, in particular, to autonomous, periodic and almost periodic in t delay differential equations. (C) 2010 Elsevier Ltd. All rights reserved.
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页码：2324 / 2333
页数：10
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