• 충청수학회지
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• 제24권4호
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• pp.883-893
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• 2011

In this paper we study h-stability of the solutions of nonlinear difference system via the notion of $n_{\infty}$-summable similarity between its variational systems. Also, we show that two concepts of h-stability and h-stability in variation for nonlinear difference systems are equivalent. Furthermore, we characterize h-stability for nonlinear difference systems by using Lyapunov functions.

• 충청수학회지
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• 제22권3호
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• pp.535-543
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• 2009

We investigate h-stability of solutions of nonlinear Volterra difference systems and linear Volterra difference systems.

• 충청수학회지
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• 제21권2호
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• pp.189-196
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• 2008

In this paper, we study h-stability for linear difference systems by using the notion of $n_{\infty}$-quasisimilarity and discrete Gronwall's inequality.

• 호남수학학술지
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• 제41권1호
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• pp.207-225
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• 2019

In the present paper, we propose some new fractional dynamical systems. These dynamical systems are associated with the variational inclusions involving difference of operators problem. The equivalence between the variational inclusion problems and the fixed point problems and as well as the resolvent equations are used to suggest fractional resolvent dynamical systems and fractional resolvent equation dynamical systems, respectively. We show that these dynamical systems converge ${\alpha}$-exponentially to the unique solution of variational inclusion problems under fewer restrictions imposed on operators and parameters. Several special cases also discussed.

• Korean Journal of Mathematics
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• 제23권4호
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• pp.665-732
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• 2015

Existence results for multiple positive solutions of two classes of boundary value problems for bilateral difference systems are established by using a fixed point theorem under convenient assumptions. It is the purpose of this paper to show that the approach to get positive solutions of boundary value problems of finite difference equations by using multi-fixed-point theorems can be extended to treat the bilateral difference systems with one-dimensional Laplacians. As an application, the sufficient conditions are established for finding multiple positive homoclinic solutions of a bilateral difference system. The methods used in this paper may be useful for numerical simulation. An example is presented to illustrate the main theorems. Further studies are proposed at the end of the paper.

• Journal of applied mathematics & informatics
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• 제34권1_2호
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• pp.35-48
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• 2016

In this paper we deal with the expressions of solutions and the periodicity nature of some systems of nonlinear difference equations with order three with nonzero real numbers initial conditions.

• 대한수학회보
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• 제39권1호
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• pp.53-62
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• 2002

We discuss the $\hbar-stability$ of perturbed Volterra difference systems by means of the resolvent matrix and discrete inequalities.

• 충청수학회지
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• 제22권4호
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• pp.635-643
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• 2009

We investigate h-stability of solutions of perturbed Volterra difference systems.

• 대한수학회보
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• 제38권1호
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• pp.101-111
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• 2001

We investigate the property of h-stability, which is an important extension of the notions of exponential stability and uniform Lipschitz stability in variation for nonlinear Volterra difference systems.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제12권2호
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• pp.93-103
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• 2005

We study some stability properties and asymptotic behavior for linear difference systems by using the results in [W. F. Trench: Linear asymptotic equilibrium and uniform, exponential, and strict stability of linear difference systems. Comput. Math. Appl. 36 (1998), no. 10-12, pp. 261-267].