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

Dong Man Im, Yoon Hoe Goo

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.


Keywords


h-stability, t1-similarity, bounded, nonlinear nonautonomous system.

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References


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DOI: http://dx.doi.org/10.11568/kjm.2016.24.4.723

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