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The number of small-amplitude limit cycles of Liénard equations

  • T. R. Blows (a1) and N. G. Lloyd (a1)

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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.

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[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.
[2]de Figueiredo, R. J. P.. On the existence of N periodic solutions of Liénard's equation. Nonlinear Anal. 7 (1983), 483499.
[3]Göbber, F. and Willamowski, K.-D.. Liapunov approach to multiple Hopf bifurcation. J. Math. Anal. Appl. 71 (1979), 333350.
[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), 335357.
[5]Nemystkii, V. V. and Stepanov, V. V.. Qualitative Theory of Differential Equations (Princeton University Press, 1960).
[6]Staude, U.. Uniqueness of periodic solutions of the Liénard equation. In Recent Advances In Differential Equations (Academic Press, 1981).

The number of small-amplitude limit cycles of Liénard equations

  • T. R. Blows (a1) and N. G. Lloyd (a1)

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