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

Dong Man Im, Yoon Hoe Goo

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 $y'=f(t,y)$.


Keywords


uniformly Lipschitz stability, uniformly Lipschitz stability in variation, exponentially asymptotic stability, exponentially asymptotic stability in variation.

Subject classification

34D05,34D20.

Sponsor(s)



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