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Existence of periodic solutions to integro-differential equations of neutral type via limiting equations

Published online by Cambridge University Press:  24 October 2008

Jianhong Wu  and
Huaxing Xia
Jianhong Wu
Affiliation:
Department of Mathematics and Statistics, York University, North York, Ontario, CanadaM3J 1P3
Huaxing Xia
Affiliation:
Department of Mathematics, University of Alberta, Edmonton, Alberta, Canada, T6G 2G1
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Abstract

In this paper, we present some results on the existence of periodic solutions to Volterra integro-differential equations of neutral type. The main idea is to show the convergence of an equibounded sequence of periodic solutions of certain limiting equations which are of finite delay. This makes it possible to apply the existing Liapunov–Razumikhin technique for neutral equations with finite delay to obtain existence of periodic solutions of Volterra neutral integro-differential equations (of infinite delay). Some comparisons between our results and the existing ideas are also provided.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 112 , Issue 2 , September 1992 , pp. 403 - 418
Copyright
Copyright © Cambridge Philosophical Society 1992

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