Abstract
We establish necessary and sufficient conditions for hyperbolicity of periodic solutions of nonlinear functional-differential equations.
References
H.-O. Walther and A. L. Skubachevskii, Trudy Moskov. Mat. Obshch., 64 (2003), 3–53; English transl.: Trans. Moscow Math. Soc., 2003, 1–44.
S. N. Chow, O. Diekmann, and J. Mallet-Paret, Japan J. Applied Math., 2 (1985), 433–469.
S. N. Chow and H.-O. Walther, Trans. Amer. Math. Soc., 307:1 (1988), 127–142.
O. Diekmann, S. van Gils, S. M. Verduyn Lunel, and H.-O. Walther, Delay Equations: Functional, Complex, and Nonlinear Analysis, Springer-Verlag, New York, 1995.
J. K. Hale and S. M. Verduyn Lunel, Introduction to Functional Differential Equations, Springer-Verlag, New York, 1993.
J. Mallet-Paret and G. Sell, J. Differential Equations, 125 (1996), 385–440.
A. L. Skubachevskii and H.-O. Walther, J. Dynam. Differential Equations, 18:2 (2006), 257–355.
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Translated from Funktsional’nyi Analiz i Ego Prilozheniya, Vol. 41, No. 1, pp. 90–92, 2007
Original Russian Text Copyright © by N. B. Zhuravlev
Supported by the Russian Foundation for Basic Research (project no. 04-01-00256).
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Zhuravlev, N.B. A hyperbolicity criterion for periodic solutions of functional-differential equations: The case of rational periods. Funct Anal Its Appl 41, 73–75 (2007). https://doi.org/10.1007/s10688-007-0006-y
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DOI: https://doi.org/10.1007/s10688-007-0006-y