Proceedings of the Edinburgh Mathematical Society (Series 2)

Table of Contents - 2002 - Volume 45, Issue 02  

Research Article

ASYMPTOTIC STABILITY OF A NEUTRAL DIFFERENTIAL EQUATION

X. H. Tanga1 and Xingfu Zoua2

a1 Department of Applied Mathematics, Central South University, Changsha, Hunan 410083, China (xhtang@public.cs.hn.cn)

a2 Department of Mathematics and Statistics, Memorial University of Newfoundland, St John’s, NF, Canada A1C 5S7 (xzou@math.mun.ca)

Abstract

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

(Received March 09 2001)

Keywords

  • uniform stability;
  • asymptotic behaviour;
  • neutral delay differential equation