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On the existence of periodic solutions for autonomous retarded functional differential equations on R2

Published online by Cambridge University Press:  14 November 2011

J. G. Dos Reis  and
R. L. S. Baroni
J. G. Dos Reis
Affiliation:
Faculdade de Medicina de Ribeirão Preto, Departamento de Matemática, Universidade de São Paulo, 14.100, Ribeirão Preto, São Paulo, Brasil
R. L. S. Baroni
Affiliation:
Faculdade de Filosofia, Ciências e Letras de Ribeirão Preto, Departamento de Matemática, Universidade de São Paulo, 14.100, Ribeirão Preto, São Paulo, Brasil
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Synopsis

Let Ca be the set of all the continuous functions from the interval [−r, 0] on the sphere of radius a, on the plane. We prove, under certains conditions, that a retarded autonomous differential equation that leaves Ca invariant has a non-constant periodic solution.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 102 , Issue 3-4 , 1986 , pp. 259 - 262
Copyright
Copyright © Royal Society of Edinburgh 1986

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References

1Hale, J. K.. Theory of functional differential equations (2nd edn) (Appl. Math. Sci. 3) (Berlin: Springer, 1977).CrossRefGoogle Scholar
2Hale, J. K.. Functional Differential Equations (Appl. Math. Sci. 3) (New York: Springer, 1971).CrossRefGoogle Scholar
3Hale, J. K., Magalhães, L. T. and Oliva, W. M.. An Introduction to Infinite Dimensional Dynamical Systems – Geometric Theory (Appl. Math. Sci. 47) (Berlin: Springer, 1984).CrossRefGoogle Scholar
4Krasnosel'skii, M. A.. Positive Solutions of Operator Equations (Groningen: Noordhoff, 1964).Google Scholar
5Nunes, W. V. L. and Táboas, P. Z.. Soluções Periódicas de Equaçóes Diferenciais Funcionais Retardadas Aut6nomas (to appear).Google Scholar