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Periodic solutions of a system of nonlinear differential equations


Author: Stanisław Sędziwy
Journal: Proc. Amer. Math. Soc. 48 (1975), 328-336
MathSciNet review: 0357980
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Abstract | References | Additional Information

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 [Enhancements On Off] (What's this?)

  • [1] M. A. Krasnosel′skiĭ, The operator of translation along the trajectories of differential equations, Translations of Mathematical Monographs, Vol. 19. Translated from the Russian by Scripta Technica, American Mathematical Society, Providence, R.I., 1968. MR 0223640
  • [2] V. A. Pliss, The existence of periodic solutions of certain non-linear systems, Soviet Math. Dokl. 2 (1959/1960), 416–418. MR 0118896
  • [3] Rolf Reissig, Note on a certain non-autonomous differential equation, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. (8) 48 (1970), 484–486 (English, with Italian summary). MR 0284655
  • [4] Rolf Reissig, Periodic solutions of a nonlinear 𝑛-th order vector differential equation, Ann. Mat. Pura Appl. (4) 87 (1970), 111–123. MR 0283309
  • [5] Rolf Reissig, Periodic solutions of a third order nonlinear differential equation, Ann. Mat. Pura Appl. (4) 92 (1972), 193–198. MR 0316827
  • [6] -, An extension of Ezeilo's result, Ann. Mat. Pura. Appl. 92 (1972), 199-210.
  • [7] J. T. Schwartz, Nonlinear functional analysis, 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; Notes on Mathematics and its Applications. MR 0433481
  • [8] Stanisław Sędziwy, Asymptotic properties of solutions of nonlinear differential equations of the higher order, Zeszyty Nauk. Uniw. Jagiello. Prace Mat. Zeszyt 11 (1966), 69–80. MR 0283314
  • [9] Stanisław Sędziwy, Asymptotic properties of solutions of a certain 𝑛th order vector differential equation, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. (8) 47 (1969), 472–475 (1970) (English, with Italian summary). MR 0271483
  • [10] Stanisław Sędziwy, Periodic solutions of differential equations in the cylindrical space, Ann. Polon. Math. 26 (1972), 335–339. MR 0308523


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1975-0357980-8
Keywords: Periodic solutions, Borsuk's theorem, system of ordinary nonlinear differential equations
Article copyright: © Copyright 1975 American Mathematical Society