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neutral delay differential equation

Proceedings of the Edinburgh Mathematical Society (1)

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ASYMPTOTIC STABILITY OF A NEUTRAL DIFFERENTIAL EQUATION
X. H. Tang, Xingfu Zou
Journal:

Proceedings of the Edinburgh Mathematical Society / Volume 45 / Issue 2 / June 2002

Published online by Cambridge University Press:

17 June 2002, pp. 333-347
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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

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ASYMPTOTIC STABILITY OF A NEUTRAL DIFFERENTIAL EQUATION