A stability theory for perturbed differential equations.
Gordon, Sheldon P. (1979)
International Journal of Mathematics and Mathematical Sciences
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Gordon, Sheldon P. (1979)
International Journal of Mathematics and Mathematical Sciences
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Liu, Xinzhi, Sivasundaram, S. (1995)
International Journal of Mathematics and Mathematical Sciences
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Grujić, L.T. (1997)
International Journal of Mathematics and Mathematical Sciences
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Kaymakçalan, Billûr (1993)
Journal of Applied Mathematics and Stochastic Analysis
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Boulbaba Ghanmi, Mohsen Dlala, Mohamed Ali Hammami (2018)
Kybernetika
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The Lyapunov's second method is one of the most famous techniques for studying the stability properties of dynamic systems. This technique uses an auxiliary function, called Lyapunov function, which checks the stability properties of a specific system without the need to generate system solutions. An important question is about the reversibility or converse of Lyapunov's second method; i. e., given a specific stability property does there exist an appropriate Lyapunov function? The main...
Liu, Xinzhi (1992)
Journal of Applied Mathematics and Stochastic Analysis
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Lakshmikantham, V., Vatsala, A.S. (1999)
Journal of Inequalities and Applications [electronic only]
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Venkatesulu, M., Srinivasu, P.D.N. (1991)
Journal of Applied Mathematics and Stochastic Analysis
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Lakshmikantham, V., Leela, S., Vasundhara Devi, J. (1999)
Journal of Inequalities and Applications [electronic only]
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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.
Sivasundaram, S., Vassilyev, S. (2000)
Journal of Applied Mathematics and Stochastic Analysis
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Liu, Kaien, Yang, Guowei (2008)
Journal of Inequalities and Applications [electronic only]
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Burton, T.A., Somolinos, Alfredo (1999)
Electronic Journal of Qualitative Theory of Differential Equations [electronic only]
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