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http://dx.doi.org/10.11568/kjm.2016.24.1.1

UNIFORMLY LIPSCHITZ STABILITY AND ASYMPTOTIC PROPERTY OF PERTURBED FUNCTIONAL DIFFERENTIAL SYSTEMS  

Im, Dong Man (Department of Mathematics Education Cheongju University)
Goo, Yoon Hoe (Department of Mathematics Hanseo University)
Publication Information
Korean Journal of Mathematics / v.24, no.1, 2016 , pp. 1-13 More about this Journal
Abstract
This paper shows that the solutions to the perturbed functional dierential system $$y^{\prime}=f(t,y)+{\int_{t_0}^{t}}g(s,y(s),Ty(s))ds$$ have uniformly Lipschitz stability and asymptotic property. To sRhow these properties, we impose conditions on the perturbed part ${\int_{t_0}^{t}}g(s,y(s),Ty(s))ds$ and the fundamental matrix of the unperturbed system $y^{\prime}=f(t,y)$.
Keywords
uniformly Lipschitz stability; uniformly Lipschitz stability in variation; exponentially asymptotic stability; exponentially asymptotic stability in variation;
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Times Cited By KSCI : 4  (Citation Analysis)
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