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 CMFD, 2007, Volume 21, Pages 37–61 (Mi cmfd76)

Hyperbolicity criterion for periodic solutions of functional-differential equations with several delays

N. B. Zhuravlev

Peoples Friendship University of Russia

Abstract: In this paper, a hyperbolicity criterion for periodic solutions of nonlinear functional-differential equations is constructed in terms of zeros of the characteristic function. In the earlier papers in this area, necessary and sufficient conditions were different from each other. Moreover, it was assumed that if the period of the investigated solution is irrational, then that solution admits a rational approximation. In this paper, we obtain necessary and sufficient conditions of the hyperbolicity. It is proved (and the proof is constructive) that a rational approximation exists for any irrational period. All the results are obtained for the case of several rational delays.

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English version:
Journal of Mathematical Sciences, 2008, 153:5, 683–709

Bibliographic databases:

UDC: 517.9

Citation: N. B. Zhuravlev, “Hyperbolicity criterion for periodic solutions of functional-differential equations with several delays”, Proceedings of the Seminar on Differential and Functional Differential Equations supervised by A. L. Skubachevskii (Peoples' Friendship University of Russia), CMFD, 21, PFUR, M., 2007, 37–61; Journal of Mathematical Sciences, 153:5 (2008), 683–709

Citation in format AMSBIB
\Bibitem{Zhu07} \by N.~B.~Zhuravlev \paper Hyperbolicity criterion for periodic solutions of functional-differential equations with several delays \inbook Proceedings of the Seminar on Differential and Functional Differential Equations supervised by A.~L.~Skubachevskii (Peoples' Friendship University of Russia) \serial CMFD \yr 2007 \vol 21 \pages 37--61 \publ PFUR \publaddr M. \mathnet{http://mi.mathnet.ru/cmfd76} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2336490} \zmath{https://zbmath.org/?q=an:1179.34076} \elib{https://elibrary.ru/item.asp?id=13587898} \transl \jour Journal of Mathematical Sciences \yr 2008 \vol 153 \issue 5 \pages 683--709 \crossref{https://doi.org/10.1007/s10958-008-9142-z} \scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-54249097751}