Geodesic
On bounded solutions of one class of systems of ordinary differential equations
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh spring mathematical school “Modern methods of the theory of boundary-value problems. Pontryagin readings – XXX”. Voronezh, May 3-9, 2019. Part 3, Tome 192 (2021), pp. 65-73.

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In this paper, we consider a priori estimates and examine the existence of bounded solutions for a class of systems of ordinary differential equations whose right-hand sides have an arbitrary order of growth with respect to the independent and dependent variables. For the right-hand sides of the equations, we find one-sided estimates that provide a priori estimates for bounded solutions; using the methods for calculating the rotation of vector fields and the method of periodic cuts, we are prove theorems on the existence of periodic and bounded solutions.
Keywords: one-sided estimate, bounded solution, periodic solution, a priori estimate, rotation of a vector field. 
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M. M. Kobilzoda; A. N. Naimov. On bounded solutions of one class of systems of ordinary differential equations. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh spring mathematical school “Modern methods of the theory of boundary-value problems. Pontryagin readings – XXX”. Voronezh, May 3-9, 2019. Part 3, Tome 192 (2021), pp. 65-73. http://geodesic.mathdoc.fr/item/INTO_2021_192_a6/

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