Geodesic
Nonzero Periodic Solutions of a Special System of Nonlinear Differential Equations
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the International Conference “Geometric Methods in Control Theory and Mathematical Physics: Differential Equations, Integrability, and Qualitative Theory,” Ryazan, September 15–18, 2016, Tome 148 (2018), pp. 93-100
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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.
Mots-clés : nonzero periodic solution, Jacobi matrix.
Keywords: nonlinear operator, fixed-point method, vector-valued function, vector-valued parameter, fundamental matrix of solutions, minor, rank of matrix, Lipschitz condition, vector-valued form 
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M. T. Terekhin. Nonzero Periodic Solutions of a Special System of Nonlinear Differential Equations. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the International Conference “Geometric Methods in Control Theory and Mathematical Physics: Differential Equations, Integrability, and Qualitative Theory,” Ryazan, September 15–18, 2016, Tome 148 (2018), pp. 93-100. http://geodesic.mathdoc.fr/item/INTO_2018_148_a11/

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