Abstract
We prove a theorem on the existence of nonzero periodic solution to a system of differential equations by the method of fixed point of nonlinear operator defined on a topological product of two compact sets.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Bibikov, Yu. N. Multifrequency Nonlinear Oscillations and Their Bifurcations (Leningrad Univ. Press, Leningrad, 1991) [in Russian].
Bogoliubov, N. N., Mitropol’skii, Yu. A. Asymptotic Methods in the Theory of Non-Linear Oscillations (Fizmatgiz, Moscow, 1955) [in Russian].
Demidovich, B. P. Lectures on Mathematical Theory of Stability (Nauka, Moscow, 1967) [in Russian].
Krasnosel’skii, M. A., Zabreiko, P. P. Geometrical Methods of Nonlinear Analysis (Nauka, Moscow, 1975) [in Russian].
Krasnosel’skii, M. A. Shift Operator Along Trajectories of Differential Equations (Nauka, Moscow, 1966) [in Russian].
Vainberg, M. M., Trenogin, V. A. Theory of Branching of Solutions of Non-Linear Equations (Nauka, Moscow, 1969) [in Russian].
Teryokhin M.T. “Bifurcation of Periodic Solutions of Functional-Differential Equations”, RussianMathematics 43, No. 10, 35–40 (1999).
Barbashin, E. A. Introduction to the Theory of Stability (Nauka, Moscow, 1967) [in Russian].
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © M.T. Teryokhin, O.V. Baeva, 2017, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2017, No. 5, pp. 86–96.
About this article
Cite this article
Teryokhin, M.T., Baeva, O.V. Periodic solutions to nonlinear nonautonomous system of differential equations. Russ Math. 61, 73–82 (2017). https://doi.org/10.3103/S1066369X17050103
Received:
Published:
Issue Date:
DOI: https://doi.org/10.3103/S1066369X17050103