Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory
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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 2018, Volume 148, Pages 93–100 (Mi into307)  
Nonzero Periodic Solutions of a Special System of Nonlinear Differential Equations

M. T. Terekhin

Ryazan State University S. A. Esenin
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Abstract: We prove a theorem on the existence of a nonzero periodic solution of a system of differential equations using the fixed-point method for a nonlinear operator defined on the product of two compact sets.
Keywords: nonzero periodic solution, nonlinear operator, fixed-point method, vector-valued function, vector-valued parameter, fundamental matrix of solutions, minor, rank of matrix, Lipschitz condition, vector-valued form, Jacobi matrix.
English version:
Journal of Mathematical Sciences (New York), 2020, Volume 248, Issue 4, Pages 467–475
DOI: https://doi.org/10.1007/s10958-020-04887-x
Bibliographic databases:
Document Type: Article
UDC: 517.925
MSC: 34C25, 34C99
Language: Russian
Citation: M. T. Terekhin, “Nonzero Periodic Solutions of a Special System of Nonlinear Differential Equations”, Proceedings of the International Conference “Geometric Methods in Control Theory and Mathematical Physics: Differential Equations, Integrability, and Qualitative Theory,” Ryazan, September 15–18, 2016, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 148, VINITI, M., 2018, 93–100; J. Math. Sci. (N. Y.), 248:4 (2020), 467–475
Citation in format AMSBIB
\Bibitem{Ter18}
\by M.~T.~Terekhin
\paper Nonzero Periodic Solutions of a Special System of Nonlinear Differential Equations
\inbook Proceedings of the International Conference ``Geometric Methods in Control Theory and Mathematical Physics: Differential Equations, Integrability, and Qualitative Theory,'' Ryazan, September 15--18, 2016
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2018
\vol 148
\pages 93--100
\publ VINITI
\publaddr M.
\mathnet{http://mi.mathnet.ru/into307}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3847712}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2020
\vol 248
\issue 4
\pages 467--475
\crossref{https://doi.org/10.1007/s10958-020-04887-x}
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