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 Tr. Mat. Inst. Steklova, 2007, Volume 256, Pages 148–171 (Mi tm460)

Hyperbolicity of Periodic Solutions of Functional Differential Equations with Several Delays

N. B. Zhuravlev, A. L. Skubachevskii

Peoples Friendship University of Russia

Abstract: We study conditions for the hyperbolicity of periodic solutions to nonlinear functional differential equations in terms of the eigenvalues of the monodromy operator. The eigenvalue problem for the monodromy operator is reduced to a boundary value problem for a system of ordinary differential equations with a spectral parameter. This makes it possible to construct a characteristic function. We prove that the zeros of this function coincide with the eigenvalues of the monodromy operator and, under certain additional conditions, the multiplicity of a zero of the characteristic function coincides with the algebraic multiplicity of the corresponding eigenvalue.

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English version:
Proceedings of the Steklov Institute of Mathematics, 2007, 256, 136–159

Bibliographic databases:

UDC: 517.9

Citation: N. B. Zhuravlev, A. L. Skubachevskii, “Hyperbolicity of Periodic Solutions of Functional Differential Equations with Several Delays”, Dynamical systems and optimization, Collected papers. Dedicated to the 70th birthday of academician Dmitrii Viktorovich Anosov, Tr. Mat. Inst. Steklova, 256, Nauka, MAIK «Nauka/Inteperiodika», M., 2007, 148–171; Proc. Steklov Inst. Math., 256 (2007), 136–159

Citation in format AMSBIB
\Bibitem{ZhuSku07} \by N.~B.~Zhuravlev, A.~L.~Skubachevskii \paper Hyperbolicity of Periodic Solutions of Functional Differential Equations with Several Delays \inbook Dynamical systems and optimization \bookinfo Collected papers. Dedicated to the 70th birthday of academician Dmitrii Viktorovich Anosov \serial Tr. Mat. Inst. Steklova \yr 2007 \vol 256 \pages 148--171 \publ Nauka, MAIK «Nauka/Inteperiodika» \publaddr M. \mathnet{http://mi.mathnet.ru/tm460} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2336898} \zmath{https://zbmath.org/?q=an:1169.34048} \elib{http://elibrary.ru/item.asp?id=9482613} \transl \jour Proc. Steklov Inst. Math. \yr 2007 \vol 256 \pages 136--159 \crossref{https://doi.org/10.1134/S0081543807010087} \elib{http://elibrary.ru/item.asp?id=13535028} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-34248342236} 

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This publication is cited in the following articles:
1. N. B. Zhuravlev, “Hyperbolicity criterion for periodic solutions of functional-differential equations with several delays”, Journal of Mathematical Sciences, 153:5 (2008), 683–709
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