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The number of small-amplitude limit cycles of Liénard equations

Published online by Cambridge University Press:  24 October 2008

T. R. Blows  and
N. G. Lloyd
T. R. Blows
Affiliation:
Department of Pure Mathematics, The University College of Wales, Aberystwyth, Dyfed
N. G. Lloyd
Affiliation:
Department of Pure Mathematics, The University College of Wales, Aberystwyth, Dyfed
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Extract

We consider second order differential equations of Liénard type:

Such equations have been very widely studied and arise frequently in applications. There is an extensive literature relating to the existence and uniqueness of periodic solutions: the paper of Staude[6] is a comprehensive survey. Our interest is in the number of periodic solutions of such equations.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 95 , Issue 2 , March 1984 , pp. 359 - 366
Copyright
Copyright © Cambridge Philosophical Society 1984

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References

REFERENCES

[1]Blows, T. R. and Lloyd, N. G.. The number of limit cycles of certain polynomial differential systems. To appear in Proc. Roy. Soc. Edinburgh Sect. A.Google Scholar
[2]de Figueiredo, R. J. P.. On the existence of N periodic solutions of Liénard's equation. Nonlinear Anal. 7 (1983), 483–499.CrossRefGoogle Scholar
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[4]Lins, A., de Melo, W. and Pugh, C. C.. On Liénard's equation. In Geometry and Topology (Rio de Janeiro, 1976). Lecture Notes in Mathematics, no. 597 (Springer-Verlag 1977), 335–357.CrossRefGoogle Scholar
[5]Nemystkii, V. V. and Stepanov, V. V.. Qualitative Theory of Differential Equations (Princeton University Press, 1960).Google Scholar
[6]Staude, U.. Uniqueness of periodic solutions of the Liénard equation. In Recent Advances In Differential Equations (Academic Press, 1981).Google Scholar