Perron-type stability theorems for neutral equations

被引：30

作者：

Burton, TA ^{[1
]}

机构：

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

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2003年 / 55卷 / 03期

关键词：

fixed points; stability; neutral equations; Perron theorem;

D O I：

10.1016/S0362-546X(03)00240-2

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we present two Perron-type asymptotic stability results for a neutral functional differential equation of the form x'(t) = Sx(t) + Px(t - r) + d/dt Q(t, x(t)) + G(t, x(t)), when the linear part (x'(t) = Sx(t) + Px(t - r)) is asymptotically stable. In particular, Q and G are allowed to be unbounded functions of t and Q need not be differentiable. The results are based on Krasnoselskii's fixed point theorem. It is to be emphasized that, unlike Perron, we obtain only asymptotic stability because of the unboundedness of Q and G. (C) 2003 Elsevier Ltd. All rights reserved.

引用

页码：285 / 297

页数：13

共 11 条

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