Korean J. Math. Vol. 24 No. 4 (2016) pp.723-736
DOI: https://doi.org/10.11568/kjm.2016.24.4.723

Boundedness in nonlinear perturbed differential systems via $t_{\infty}$-similarity

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Published: Dec 30, 2016
Keywords:
h-stability, t1-similarity, bounded, nonlinear nonautonomous system.
Mathematics Subject Classification:
34D10, 34D20

Main Article Content

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 nonlinear perturbed differential system
$$
y'=f(t,y)+\int_{t_0}^tg(s,y(s))ds+h(t,y(t),Ty(t))
$$
have bounded properties. To show the bounded properties, we impose conditions on the perturbed part
$\int_{t_0}^tg(s,y(s))ds$, $h(t,y(t),Ty(t))$, and on the fundamental matrix of the unperturbed system $y'=f(t,y)$ using the notion of $h$-stability.



Article Details

Supporting Agencies

Lee Man Seab Mokwon Unversity Department of Mathematics Kim Hark Man Chungnam University Jung Soon Mo Hongik University Department of liberal Mathematics

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