Nonzero Periodic Solutions of a Special System of Nonlinear Differential Equations

Abstract

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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References

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Correspondence to M. T. Terekhin.

Additional information

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

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Keywords and phrases

  • 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

AMS Subject Classification

  • 34C25
  • 34C99