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Topological transversality and periodic solutions of neutral functional differential equations

Published online by Cambridge University Press:  14 November 2011

Jianhong Wu ,
Huaxing Xia  and
Bo Zhang
Jianhong Wu
Affiliation:
Department of Mathematics and Statistics, York University, North York, Ontario, CanadaM3J 1P3
Huaxing Xia
Affiliation:
Department of Mathematics and Statistics, York University, North York, Ontario, CanadaM3J 1P3
Bo Zhang
Affiliation:
Department of Mathematics and Computer Science, Fayetteville State University, Fayetteville, NC 28301, USA
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Extract

In this paper, we study the existence of periodic solutions of neutral functional differential equations (NFDEs). A topological transversality theorem is used to obtain fixed points of certain nonlinear compact operators, which correspond to periodic solutions of the original differential equations. The method relies on a priori bounds on periodic solutions to a family of appropriately constructed NFDEs. A general existence theorem is proved and several illustrative examples are given where we use Liapunov-like functions in deriving such a priori bounds on periodic solutions. Due to the topological nature of the approach, the theorem applies as well to NFDEs of mixed type and NFDEs with state-dependent delay. Some comparisons between our results and the existing ones are also provided.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 129 , Issue 1 , 1999 , pp. 199 - 220
Copyright
Copyright © Royal Society of Edinburgh 1999

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