• Bulletin of the Korean Mathematical Society
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• v.50 no.5
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• pp.1555-1565
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• 2013

In this paper, some new generalized discrete Halanay inequalities are established. On the basis of these new established inequalities, we obtain the attracting set and the global asymptotic stability of the nonlinear discrete systems. Our results established here extend the main results in [R. P. Agarwal, Y. H. Kim, and S. K. Sen, New discrete Halanay inequalities: stability of difference equations, Commun. Appl. Anal. 12 (2008), no. 1, 83-90] and [S. Udpin and P. Niamsup, New discrete type inequalities and global stability of nonlinear difference equations, Appl. Math. Lett. 22 (2009), no. 6, 856-859].

• The Pure and Applied Mathematics
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• v.4 no.2
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• pp.167-173
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• 1997

In this paper, we investigated several asymptotic stability properties of the system for the type of dy/dt = $h(t)^{-1}F(t_1, k(t)y(t))$.

• Journal of Institute of Control, Robotics and Systems
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• v.13 no.3
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• pp.187-191
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• 2007

We analyze the stability property of a class of nonlinear time-delay systems. We show that the state variable is bounded both below and above, and the lower and upper bounds of the state are obtained in terms of a system parameter by using the comparison lemma. We establish a time-delay independent sufficient condition for the global asymptotic stability by employing a Lyapunov-Krasovskii functional obtained from a change of the state variable. The simulation results illustrate the validity of the sufficient condition for the global asymptotic stability.

• Journal of applied mathematics & informatics
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• v.33 no.5_6
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• pp.687-697
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• 2015

This paper shows that the solutions to the perturbed nonlinear functional differential system

• Journal of applied mathematics & informatics
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• v.6 no.1
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• pp.185-196
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• 1999

This paper is concerned with investigating the global asymptotic behavior of the solution to a nonlinear wave equation with variable coefficients. noreover an estimate of the rate of decay of the solution is obtained.

• Communications of the Korean Mathematical Society
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• v.26 no.1
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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.

• Journal of the Chungcheong Mathematical Society
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• v.29 no.1
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• pp.1-11
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• 2016

This paper shows that the solutions to nonlinear perturbed functional differential system $$y^{\prime}=f(t,y)+{\int}^t_{t_0}g(s,y(s),Ty(s))ds+h(t,y(t))$$ have the asymptotic property by imposing conditions on the perturbed part ${\int}^t_{t_0}g(s,y(s),Ty(s))ds,h(t,y(t))$ and on the fundamental matrix of the unperturbed system y' = f(t, y).

• Bulletin of the Korean Mathematical Society
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• v.55 no.1
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• pp.319-330
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• 2018

This paper is concerned with the global asymptotic stability of strong solutions for a class of semilinear evolution equations with nonlocal initial conditions on infinite interval. The discussion is based on analytic semigroups theory and the gradually regularization method. The results obtained in this paper improve and extend some related conclusions on this topic.

• Journal of applied mathematics & informatics
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• v.18 no.1_2
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• pp.405-417
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• 2005

In this paper, the oscillation and asymptotic stability behavior of a third order linear impulsive equation are investigated. A lemma is presented to deal with the sign relation of the nonoscillatory solutions and their derived functions. By the lemma explicit sufficient conditions are obtained for all solutions either oscillating or asymptotically tending to zero. Two illustrative examples are proposed to demonstrate the effectiveness of the conditions.

• Journal of Institute of Control, Robotics and Systems
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• v.14 no.6
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• pp.554-557
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• 2008

We analyze the stability property of a class of nonlinear time-delay systems with time-varying delays. We present a time-delay independent sufficient condition for the global asymptotic stability. In order to prove the sufficient condition, we exploit the inherent property of the considered systems instead of applying the Krasovskii or Razumikhin stability theory that may cause the mathematical difficulty of analysis. We prove the sufficient condition by constructing two sequences that represent the lower and upper bound variations of system state in time, and showing the two sequences converge to an identical point, which is the equilibrium point of the system. The simulation results illustrate the validity of the sufficient condition for the global asymptotic stability.