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Journal of Mathematical Sciences

, Volume 153, Issue 5, pp 683–709 | Cite as

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

  • N. B. Zhuravlev
Article
  • 22 Downloads

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.

Keywords

Periodic Solution Rational Approximation Operator Versus Delay Equation Algebraic Multiplicity 
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Copyright information

© Springer Science+Business Media, Inc. 2008

Authors and Affiliations

  1. 1.Department of Differential Equations and Mathematical PhysicsPeoples’ Friendship University of RussiaMoscowRussia

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