NONOSCILLATION AND EXPONENTIAL STABILITY OF DELAY DIFFERENTIAL EQUATIONS WITH OSCILLATING COEFFICIENTS

被引：10

作者：

Berezansky, L. ^{[1
]}

Braverman, E. ^{[2
]}

机构：

[1] Ben Gurion Univ Negev, Dept Math, IL-84105 Beer Sheva, Israel

[2] Univ Calgary, Dept Math & Stat, Calgary, AB T2N 1N4, Canada

来源：

JOURNAL OF DYNAMICAL AND CONTROL SYSTEMS | 2009年 / 15卷 / 01期

基金：

加拿大自然科学与工程研究理事会;

关键词：

Linear delay equations; exponential stability; positive fundamental function; oscillating coefficients; LINEAR-SYSTEMS; POSITIVE SOLUTIONS;

D O I：

10.1007/s10883-008-9058-4

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

We prove that under some additional conditions, the nonoscillation of the scalar delay differential equation x(over dot)(t) + (m)Sigma(k=1) a(k)(t)x(h(k)(t)) = 0 implies the exponential stability. New nonoscillation conditions are obtained for equations with positive and negative coefficients and for equations of arbitrary signs. As an example, we present an exponentially stable equation with two delays and two oscillating coefficients.

引用

页码：63 / 82

页数：20

共 20 条

[1]

AGARWAL RP, 1998, POSITIVE SOLUTIONS

[2]

Azbelev N. V., 2003, Stability and Control: Theory, Methods and Applications, V20

[3]

AZBELEV NV, 1991, DIFF EQUAT+, V27, P1165

[4]

AZBELEV NV, 1993, DIFF EQUAT+, V29, P153