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/

[3] Krasnoselskii M. A., Operator sdviga po traektoriyam differentsialnykh uravnenii, Nauka, M., 1966

[4] Krasnoselskii M. A., Zabreiko P. P., Geometricheskie metody nelineinogo analiza, Nauka, M., 1975

[5] Mukhamadiev E., “K teorii periodicheskikh reshenii sistem obyknovennykh differentsialnykh uravnenii”, Dokl. AN SSSR., 194:11 (1970), 510–513

[6] Mukhamadiev E., “K teorii ogranichennykh reshenii obyknovennykh differentsialnykh uravnenii”, Differ. uravn., 10:4 (1974), 635–646

[7] Mukhamadiev E., “Issledovaniya po teorii periodicheskikh i ogranichennykh reshenii differentsialnykh uravnenii”, Mat. zametki., 30:3 (1981), 713–722

[8] Mukhamadiev E., Naimov A. N., Sattorov A. Kh., “Ob ogranichennykh resheniyakh odnogo klassa giperbolicheskikh uravnenii na ploskosti”, Differ. uravn., 52:1 (2016), 86–93

[9] Mukhamadiev E., Naimov A. N., Sattorov A. Kh., “Analog teoremy Bolya dlya odnogo klassa lineinykh differentsialnykh uravnenii v chastnykh proizvodnykh”, Ufim. mat. zh., 9:1 (2017), 75–88