Extendability of solutions of autonomous polynomial differential systems

V. V. Amel'kin^a, V. Yu. Tyshchenko<sup>b

a</sup> Belorussian State University, 4 Nezavisimosti ave., Minsk, 220030 Republic of Belarus
^b Grodno State University, 22 Oszeshko str., Grodno, 230023 Republic of Belarus

Abstract: We consider real and complex autonomous polynomial differential systems, both ordinary and exact. It is proved that in case of general situation the solutions of the given systems are not infinitely continuable on all independent variables. Examples are given.

Keywords: ordinary autonomous system of the differential equations, quite solvable autonomous system of the exact equations, continuability of the solutions.

UDC: 517.925

Received: 11.01.2019
Revised: 11.01.2019
Accepted: 27.03.2019

DOI: 10.26907/0021-3446-2020-2-10-21

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2020, 64:2, 8–18

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