We prove a theorem on the existence of a nonzero periodic solution to a system of differential equations using the fixed-point method for a nonlinear operator defined on the product of two compact sets.
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Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory, Vol. 148, Proceedings of the International Conference “Geometric Methods in Control Theory and Mathematical Physics: Differential Equations, Integrability, and Qualitative Theory” (Ryazan, September 15–18, 2016), 2018.
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Terekhin, M.T. Nonzero Periodic Solutions of a Special System of Nonlinear Differential Equations. J Math Sci 248, 467–475 (2020). https://doi.org/10.1007/s10958-020-04887-x
Keywords and phrases
- nonzero periodic solution
- nonlinear operator
- fixed-point method
- vector-valued function
- vector-valued parameter
- fundamental matrix of solutions
- rank of matrix
- Lipschitz condition
- vector-valued form
- Jacobi matrix
AMS Subject Classification