The number of periodic solutions of polynomial differential equations

Pleiades Publishing Ltd - Tập 64 - Trang 622-628 - 1998
A. A. Panov1
1Moscow Institute for Geodesy, Aerial Photography, and Cartography, USSR

Tóm tắt

We estimate the number of periodic solutions for special classes ofnth-order ordinary differential equations with variable coefficients.

Tài liệu tham khảo

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).