For a state of equilibrium of an autonomous system of differential equations, we propose discrete conditions for stability and asymptotic stability in the sense of Lyapunov.
References
N. Rouche, P. Habets, and M. Laloy, Stability Theory by Liapunov’s Direct Method, Springer, New York (1977).
Yu. V. Sharko, “Discrete conditions for Lyapunov stability,” Zb. Prats’ Inst. Mat. NAN Ukr., 2, No. 3, 279–288 (2005).
M. W. Hirsch, Differential Topology, Springer, New York (1976).
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 62, No. 9, pp. 1294–1296, September, 2010.
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Sharko, Y.V. Quantization of Lyapunov functions. Ukr Math J 62, 1502–1505 (2011). https://doi.org/10.1007/s11253-011-0445-8
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DOI: https://doi.org/10.1007/s11253-011-0445-8