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ASYMPTOTIC STABILITY OF A NEUTRAL DIFFERENTIAL EQUATION

Published online by Cambridge University Press:  17 June 2002

X. H. Tang  and
Xingfu Zou
X. H. Tang
Affiliation:
Department of Applied Mathematics, Central South University, Changsha, Hunan 410083, China ([email protected])
Xingfu Zou
Affiliation:
Department of Mathematics and Statistics, Memorial University of Newfoundland, St John’s, NF, Canada A1C 5S7 ([email protected])
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Abstract

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The uniform stability of the zero solution and the asymptotic behaviour of all solutions of the neutral delay differential equation

$$ [x(t)-P(t)x(t-\tau)]'+Q(t)x(t-\sigma)=0,\quad t\ge t_0, $$

are investigated, where $\tau,\sigma\in(0,\infty)$, $P\in C([t_0,\infty),\mathbb{R})$, and $Q\in C([t_0,\infty), [0,\infty))$. The obtained sufficient conditions improve the existing results in the literature.

AMS 2000 Mathematics subject classification: Primary 34K20; 34K15; 34K40

Keywords

uniform stabilityasymptotic behaviourneutral delay differential equation
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 45 , Issue 2 , June 2002 , pp. 333 - 347
Copyright
Copyright © Edinburgh Mathematical Society 2002