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

#### 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

#### Full Text:

PDF#### References

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

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