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July/August 2009 Periodic solutions of delay equations with several fixed delays
Benjamin Kennedy
Differential Integral Equations 22(7/8): 679-724 (July/August 2009).

Abstract

We present an existence result for periodic solutions of autonomous differential delay equations with several fixed delays \begin{eqnarray*} x'(t) = \sum_{i=1}^D f_i (x(t - d_i)), \end{eqnarray*} where the functions $f_i$ are close to two-valued step functions $h_i$. We give conditions under which existence of periodic solutions of the more tractable problem $$ y'(t) = \sum_{i=1}^D h_i (y(t - d_i)) $$ implies the existence of similar periodic solutions of the original problem. Our approach is to show that an analog of a Poincaré map has non-trivial fixed-point index.

Citation

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Benjamin Kennedy. "Periodic solutions of delay equations with several fixed delays." Differential Integral Equations 22 (7/8) 679 - 724, July/August 2009.

Information

Published: July/August 2009
First available in Project Euclid: 20 December 2012

zbMATH: 1240.34317
MathSciNet: MR2532117

Subjects:
Primary: 34K13

Rights: Copyright © 2009 Khayyam Publishing, Inc.

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Vol.22 • No. 7/8 • July/August 2009
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