Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Periodic solutions of a system of nonlinear differential equations
HTML articles powered by AMS MathViewer

by Stanisław Sędziwy
Proc. Amer. Math. Soc. 48 (1975), 328-336
DOI: https://doi.org/10.1090/S0002-9939-1975-0357980-8

Abstract:

The paper consists of a study of the existence of periodic solutions of a system of differential equations using Borsuk’s theorem on odd mappings. Applications are given to $n$th order nonlinear vector differential systems and $n$th order nonlinear scalar differential equations.
References
  • M. A. Krasnosel′skiĭ, The operator of translation along the trajectories of differential equations, Translations of Mathematical Monographs, Vol. 19, American Mathematical Society, Providence, R.I., 1968. Translated from the Russian by Scripta Technica. MR 0223640
  • V. A. Pliss, The existence of periodic solutions of certain non-linear systems, Soviet Math. Dokl. 2 (1959/1960), 416–418. MR 0118896
  • Rolf Reissig, Note on a certain non-autonomous differential equation, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Nat. (8) 48 (1970), 484–486 (English, with Italian summary). MR 284655
  • Rolf Reissig, Periodic solutions of a nonlinear $n$-th order vector differential equation, Ann. Mat. Pura Appl. (4) 87 (1970), 111–123. MR 283309, DOI 10.1007/BF02411974
  • Rolf Reissig, Periodic solutions of a third order nonlinear differential equation, Ann. Mat. Pura Appl. (4) 92 (1972), 193–198. MR 316827, DOI 10.1007/BF02417946
  • —, An extension of Ezeilo’s result, Ann. Mat. Pura. Appl. 92 (1972), 199-210.
  • J. T. Schwartz, Nonlinear functional analysis, Notes on Mathematics and its Applications, Gordon and Breach Science Publishers, New York-London-Paris, 1969. Notes by H. Fattorini, R. Nirenberg and H. Porta, with an additional chapter by Hermann Karcher. MR 0433481
  • Stanisław Sędziwy, Asymptotic properties of solutions of nonlinear differential equations of the higher order, Zeszyty Nauk. Uniw. Jagielloń. Prace Mat. 11 (1966), 69–80. MR 283314
  • Stanisław Sędziwy, Asymptotic properties of solutions of a certain $n$th order vector differential equation, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Nat. (8) 47 (1969), 472–475 (1970) (English, with Italian summary). MR 271483
  • Stanisław Sędziwy, Periodic solutions of differential equations in the cylindrical space, Ann. Polon. Math. 26 (1972), 335–339. MR 308523, DOI 10.4064/ap-26-3-335-339
Bibliographic Information
  • © Copyright 1975 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 48 (1975), 328-336
  • DOI: https://doi.org/10.1090/S0002-9939-1975-0357980-8
  • MathSciNet review: 0357980