Abstract
We estimate the number of periodic solutions for special classes ofnth-order ordinary differential equations with variable coefficients.
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References
V. I. Arnol'd and Yu. S. Il'yashenko, “Ordinary differential equations,” in:Dynamical Systems. Itogi Nauki i Tekhniki. Modern Problems in Mathematics. Fundamental Directions [in Russian], Vol. 1, VINITI, Moscow (1985), pp. 7–149.
V. A. Pliss, “The number of periodic solutions of equations with polynomial right-hand side,”Dokl. Akad. Nauk SSSR [Soviet Math. Dokl.],127, No. 5, 965–968 (1959).
S. Shahshahani, “Periodic solutions of polynomial first-order differential equations,”Nonlinear Anal.,5, No. 2, 157–165 (1981).
V. V. Stepanov,Differential Equations [in Russian], Gostekhizdat, Moscow (1952).
V. I. Arnol'd,Mathematical Methods of Classical Mechanics [in Russian], Nauka, Moscow (1989).
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Translated fromMatematicheskie Zametki, Vol. 64, No. 5, pp. 720–727, November, 1998.
The author thanks Yu. S. Il'yashenko for setting the problems, permanent advice, and overall support. The author is also thankful to D. A. Panov for numerous discussions.
This research was supported by the CRDF Foundation under grant MR1-220, by the INTAS Foundation under grant No. 93-05-07, and by the Russian Foundation for Basic Research under grant No. 95-01-01258.
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Panov, A.A. The number of periodic solutions of polynomial differential equations. Math Notes 64, 622–628 (1998). https://doi.org/10.1007/BF02316287
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DOI: https://doi.org/10.1007/BF02316287