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Periodic solutions to functional differential equations

Published online by Cambridge University Press:  14 November 2011

O. A. Arino ,
T. A. Burton  and
J. R. Haddock
O. A. Arino
Affiliation:
Departement de Mathematiques, Faculté des Sciences, Avenue L. Sallenave, 6400 Pau, France
T. A. Burton
Affiliation:
Department of Mathematics, Southern Illinois University, Carbondale, Illinois 62901, U.S.A
J. R. Haddock
Affiliation:
Department of Mathematical Sciences, Memphis State University, Memphis, Tennessee 38152, U.S.A
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Synopsis

We consider a system of functional differential equations

where G: R × B → Rn is T periodic in t and B is a certain phase space of continuous functions that map (−∞, 0[ into Rn. The concepts of B-uniform boundedness and B-uniform ultimate boundedness are introduced, and sufficient conditions are given for the existence of a T-periodic solution to (1.1). Several examples are given to illustrate the main theorem.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 101 , Issue 3-4 , 1985 , pp. 253 - 271
Copyright
Copyright © Royal Society of Edinburgh 1985

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