• 대한수학회논문집
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• 제26권1호
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• pp.37-49
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• 2011

We investigate the asymptotic equivalence for linear differential systems by means of the notions of $t_{\infty}$-similarity and strong stability.

• 충청수학회지
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• 제22권3호
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• pp.545-556
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• 2009

We show that two notions of asymptotic equilibrium and asymptotic equilibrium in variation for nonlinear differential systems are equivalent via $t_{\infty}$-similarity of associated variational systems. Moreover, we study the asymptotic equivalence between nonlinear system and its variational system.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제20권3호
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• pp.223-232
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• 2013

Alexseev's formula generalizes the variation of constants formula and permits the study of a nonlinear perturbation of a system with certain stability properties. In recent years M. Pinto introduced the notion of $h$-stability. S.K. Choi et al. investigated $h$-stability for the nonlinear differential systems using the notion of $t_{\infty}$-similarity. Applying these two notions, we study bounds for solutions of the perturbed differential systems.

• 대한수학회지
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• 제53권5호
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• pp.1115-1131
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• 2016

In this paper we develop useful relations which estimate the difference between the solutions of nonlinear impulsive differential systems with different initial values. Then we obtain the converse h-stability theorem of Massera's type for the nonlinear impulsive systems by employing the $t_{\infty}$-similarity of the associated impulsive variational systems and relations.

• Journal of applied mathematics & informatics
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• 제30권1_2호
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• pp.279-287
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• 2012

In this paper, we investigate bounds for solutions of the nonlinear differential systems using the notion of $t_{\infty}$-similarity.

• Korean Journal of Mathematics
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• 제24권4호
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• pp.723-736
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• 2016

This paper shows that the solutions to nonlinear perturbed differential system $$y^{\prime}= f(t,y)+{\int_{t_{0}}^{t}g(s,y(s))ds+h(t,y(t),Ty(t))$$ have bounded properties. To show the bounded properties, we impose conditions on the perturbed part ${\int_{t_{0}}^{t}g(s,y(s))ds,\;h(t, y(t),\;Ty(t))$, and on the fundamental matrix of the unperturbed system y' = f(t, y) using the notion of h-stability.

• Journal of applied mathematics & informatics
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• 제32권1_2호
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• pp.247-254
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• 2014

In this paper, we investigate bounds for solutions of nonlinear perturbed differential systems.

• 충청수학회지
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• 제28권1호
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• pp.73-82
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• 2015

In this paper, we investigate h-stability and bounds for solutions of the the functional perturbed differential systems

• 충청수학회지
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• 제26권3호
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• pp.605-613
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• 2013

In this paper, we investigate bounds for solutions of perturbed nonlinear differential systems.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제18권4호
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• pp.337-344
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• 2011

In this paper, we investigate h-stability of the nonlinear perturbed differential systems.