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On periodic solutions to autonomous retarded functional differential equations

Published online by Cambridge University Press:  17 April 2009

Zhanyuan Hou
Zhanyuan Hou
Affiliation:
Mathematics Department, Hebei Teacher's University, Shijiazhuang, Peoples Republic of China
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Under the assumption that Ca = C([−r, 0], Sn−1(a)) is positively invariant for a > 0, two necessary and sufficient conditions are obtained for an autonomous retarded functional differential equation to have a non-trivial periodic solution in Ca. Moreover, a feasible sufficient condition is given, which is better for n = 2 than that given by Dos Reis and Baroni.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 41 , Issue 3 , June 1990 , pp. 347 - 354
Copyright
Copyright © Australian Mathematical Society 1990

References

[1]Dos Reis, J.G. and Baroni, R.L.S., ‘On the existence of periodic solutions for autonomous retarded functional differential equations on R 2’, Proc. Royal Soc. Edinburgh Section A 102 (1986), 259–262.CrossRefGoogle Scholar
[2]Hale, J.K., Functional Differential Equations, (Appl. Math. Sci. 3) (Springer-Verlag, Berlin, Heidelberg, New York, 1971).CrossRefGoogle Scholar
[3]Hale, J.K., Theory of Functional Differential Equations, (2nd edition), (Appl. Math. Sci. 3) (Springer-Verlag, Berlin Heidelberg, New York, 1977).CrossRefGoogle Scholar
[4]Krasnosel'skii, M.A., Positive Solutions of Operator Equations (Noordhoff, Grongingen, 1964).Google Scholar