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Bifurcation of the periodic differential equations with regularisable infinity

Published online by Cambridge University Press:  14 November 2011

Guan Ke-ying
Guan Ke-ying
Affiliation:
Department of Mathematics, Beijing Institute of Aeronautics and Astronautics, P.O. Box 85, Beijing, PR China
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Extract

A class of scalar periodic differential equations x ]f(x, t, A) with regularisable infinity in which the Riccati equation is included, can be treated as autonomous systems on the torus T2. Through this geometric interpretation, the properties of the set of bifurcation points of λ (∊R) are studied. When the results obtained are applied to the Riccati equation, they can match the well-known properties of the spectral set of the corresponding Hill's equation.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 107 , Issue 3-4 , 1987 , pp. 233 - 247
Copyright
Copyright © Royal Society of Edinburgh 1987

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References

1Klingenberg, Wilhelm. A course in Differential Geometry (New York: Springer, 1978).Google Scholar
2Yuan-xun, Qin. On periodic solutions of Riccati equation. Kexue Tongbao 23 (1979), 1062–1065.Google Scholar
3Mawhin, J.. First order ordinary differential equations with several periodic solutions. Z. Angew. Math. Phys. (to appear).Google Scholar
4Lloyd, N. J.. Some one-parameter families of scalar differential equations (to appear).Google Scholar
5Guan, K. Y., Gunson, J. and Hasan, H. S.. On periodic solutions of the periodic Riccati equation (to appear).Google Scholar
6Lloyd, N. G.. The number of periodic solutions of the equation z ] z N + p 1(t)z N−1… + … + p N(t). Proc. London Math. Soc. (3) 27 (1973), 667–700.Google Scholar
7Eastham, M. S. P.. The spectral theory of periodic differential equations (Edinburgh: Scottish Academic Press, 1973).Google Scholar