Abstract
By using the variational Liapunov method, stability properties in terms of two measures for delay differential equations are discussed. In the case that the unperturbed systems are ordinary differential systems, employing auxiliary measure h*(t,x), criteria on nonuniform and uniform stability in terms of two measures for delay differential equations are established.
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References
Hale J.Theory of Differential Equations [M]. New York: Springer-Verlag, 1977.
LIU **n-zhi. Advances in stability theory of nonlinear systems [A]. In:Proceedings of International Conference on Dynamical Systems and Differential Equations [C]. Vol. E-3 Shanghai: Shanghai Jiaotong University Press, 1998.
Lakshmikantham V. Advances in UAS for functional differential equations [J].Merm Diff Equas Math Phy, 1997,12(1):131–134.
Lakshmikantham V, Leela S, Sivasundaram S. Liapunov functions on product spaces and stability theory of delay differetnial equations [J].J Math Anal Appl, 1991,154(2):391–402.
Lakshmikantham V, LIU **n-zhi.Stability Analysis in Terms of Two Measures [M]. Singapore: World Scientific, 1993.
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Communicated by Liu Zeng-rong
Foundation item: the National Natural Science Foundation of China (19831030)
Biography: Kou Chun-hai (1963-)
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Chun-hai, K., Shu-nian, Z. Stability criteria in terms of two measures for delay differential equations. Appl Math Mech 23, 311–320 (2002). https://doi.org/10.1007/BF02438338
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DOI: https://doi.org/10.1007/BF02438338