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

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. © 2008 Springer Science+Business Media, Inc.

Авторы
Издательство
Springer New York LLC
Номер выпуска
5
Язык
Английский
Страницы
683-709
Статус
Опубликовано
Том
153
Год
2008
Организации
  • 1 Department of Differential Equations and Mathematical Physics, Peoples' Friendship University of Russia, Ordzhonikidze str., 3, 117198, Moscow, Russian Federation
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