### Explicit conditions for stability of nonlinear scalar delay impulsive difference equation.

Zheng, Bo (2010)

Advances in Difference Equations [electronic only]

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Zheng, Bo (2010)

Advances in Difference Equations [electronic only]

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He, Danhua, Xu, Liguang (2009)

Journal of Inequalities and Applications [electronic only]

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Liu, Kaien, Yang, Guowei (2008)

Journal of Inequalities and Applications [electronic only]

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Alzabut, Jehad O., Abdeljawad, Thabet (2007)

Discrete Dynamics in Nature and Society

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Du, Binbin, Zhang, Xiaojie (2011)

Discrete Dynamics in Nature and Society

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Bradul, Nataliya, Shaikhet, Leonid (2007)

Discrete Dynamics in Nature and Society

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Krzysztof Ciesielski (2004)

Bulletin of the Polish Academy of Sciences. Mathematics

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Several results on stability in impulsive dynamical systems are proved. The first main result gives equivalent conditions for stability of a compact set. In particular, a generalization of Ura's theorem to the case of impulsive systems is shown. The second main theorem says that under some additional assumptions every component of a stable set is stable. Also, several examples indicating possible complicated phenomena in impulsive systems are presented.

De La Sen, M., Ibeas, A. (2008)

Discrete Dynamics in Nature and Society

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Benjelloun, K., Boukas, E.K. (1997)

Mathematical Problems in Engineering

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Erik I. Verriest (2001)

Kybernetika

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A qualitative method is explored for analyzing the stability of systems. The approach is a generalization of the celebrated Lyapunov method. Whereas classically, the Lyapunov method is based on the simple comparison theorem, deriving suitable candidate Lyapunov functions remains mostly an art. As a result, in the realm of delay equations, such Lyapunov methods can be quite conservative. The generalization is here in using the comparison theorem directly with a different scalar equation...

de la Sen, M., Ibeas, A. (2008)

Mathematical Problems in Engineering

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Abdelouaheb Ardjouni, Ahcene Djoudi (2013)

Mathematica Bohemica

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In this paper we use the fixed point method to prove asymptotic stability results of the zero solution of a generalized linear neutral difference equation with variable delays. An asymptotic stability theorem with a sufficient condition is proved, which improves and generalizes some results due to Y. N. Raffoul (2006), E. Yankson (2009), M. Islam and E. Yankson (2005).