Fixed points, stability, and exact linearization

被引：50

作者：

Burton, TA ^{[1
]}

机构：

[1] NW Res Inst, Port Angeles, WA 98362 USA

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2005年 / 61卷 / 05期

关键词：

asymptotic stability; contraction mappings; second-order delay equations;

D O I：

10.1016/j.na.2005.01.079

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the scalar equation x '' + f (t, x, x')x' + b(t)g(x(t - L)) = 0 by means of contraction mappings. Conditions are obtained to ensure that each solution (x (t), x'(t)) -> (0, 0) as t -> infinity. The conditions allow f to grow as large as I, but not as large as t(2). This is parallel to the classical result of Smith (Quart. J. Math. Oxford Ser. 12 (2) (1961) 123) for the linear equation without a delay. (c) 2005 Elsevier Ltd. All rights reserved.

引用

页码：857 / 870

页数：14

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