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Periodic solutions of polynomial non-autonomous differential equations

Published online by Cambridge University Press:  14 November 2011

J. Devlin
J. Devlin
Affiliation:
Department of Mathematics, The University College of Wales, Aberystwyth, Dyfed, SY23 3BZ, U.K.
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Extract

Let ℐN denote the set of (N + 1)-tuples of C1 ω-periodic functions; the point P = (pN,…, p1p0) ϵ ℐN is identified with the differential equation

We examine the way in which the total number of ω-periodic solutions can vary as P traverses a path in ℐN.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 123 , Issue 5 , 1993 , pp. 783 - 801
Copyright
Copyright © Royal Society of Edinburgh 1993

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References

1Alwash, M. A. M. and Lloyd, N. G.. Non-autonomous equations related to polynomial two-dimensional systems. Proc. Roy. Soc. Edinburgh Sect. A 105 (1987), 129–152.CrossRefGoogle Scholar
2Bautin, N. N.. On the number of limit cycles which appear with the variation of coefficients from an equilibrium position of focus or centre type. Trans. Amer. Math. Soc. 100 (1954), 1–19.Google Scholar
3Carbonell, M. and Llibre, J.. Limit cycles of polynomial systems with homogeneous nonlinearites (preprint, Universitat Autonoma de Barcelona, 1988).Google Scholar
4Coppel, W. A.. A simple class of quadratic systems. Differential Equations 64 (1986), 275–282.CrossRefGoogle Scholar
5Devlin, J.. Word problems related to periodic solutions of a non-autonomous system. Math. Proc. Cambridge Philos, Soc. 108 (1990), 127–151.CrossRefGoogle Scholar
6Chengzhi, Li. Non-existence of limit cycles around a weak focus of order three for any quadratic system. Chinese Ann. Math. 7B (1986), 174–190.Google Scholar
7Neto, A. Lins. On the number of solutions of the equation dx/dt, for which JC(O). Invent. Math. 59 (1980), 67–76.CrossRefGoogle Scholar
8Lloyd, N. G.. The number of periodic solutions of the equation Proc. London Math. Soc. (3) 27 (1973), 667–700.CrossRefGoogle Scholar
9Lloyd, N. G.. Small amplitude limit cycles of polynomial differential equations. In Ordinary Differential Equations and Operators eds. Everitt, W. N. and Lewis, R. T., Lecture Notes in Mathematics 1032, 346–357 (Berlin: Springer, 1982).Google Scholar
10Lloyd, N. G.. Limit cycles of certain polynomial systems. In Nonlinear Functional Analysis and Applications, ed. Singh, S. P., NATO ASI Series C 173 (1986), 317–326.CrossRefGoogle Scholar
11Pliss, V. A. P.. Nonlocal problems in the theory of oscillations (New York: Academic Press, 1966).Google Scholar