Korean J. Math. Vol. 24 No. 1 (2016) pp.1-13
DOI: https://doi.org/10.11568/kjm.2016.24.1.1

Uniformly Lipschitz stability and asymptotic property of perturbed functional differential systems

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Published: Mar 30, 2016
Keywords:
uniformly Lipschitz stability, uniformly Lipschitz stability in variation, exponentially asymptotic stability, exponentially asymptotic stability in variation.
Mathematics Subject Classification:
34D05, 34D20.

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Dong Man Im
Department of Mathematics Education Cheongju University Cheongju 360-764, Republic of Korea
Yoon Hoe Goo
Department of Mathematics Hanseo University Seosan 356-706, Republic of Korea

Abstract

This paper shows that the solutions to the perturbed functional differential system
\begin{eqnarray*}
y'=f(t,y)+\int_{t_0}^tg(s,y(s),Ty(s))ds
\end{eqnarray*}
have uniformly Lipschitz stability and asymptotic property. To show these properties, we impose conditions on the perturbed part
$\int_{t_0}^tg(s,y(s),Ty(s))ds$ and the fundamental matrix of the unperturbed system $y'=f(t,y)$.



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