2017
Том 69
№ 9

All Issues

Some criteria of the limitation of solutions of systems of nonlinear differential equations

Skripnik V. P.

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Abstract

The systems of nonlinear differential equations 1, 2, 3 are considered in this paper.
These systems are not always solved with respect to the highest derivatives. For systems 1 and 2 some criteria of limitation or tendency to zero of the solutions for $t \rightarrow \infty$ are proved. For the system 1 the criterion of limitation of the solutions and their derivatives is proved. The theorem on the average value is used to establish these theorems.
The estimations of the solutions depend on the initial conditions, characteristic numbers of symmetric parts and the norms of some matrices.

Citation Example: Skripnik V. P. Some criteria of the limitation of solutions of systems of nonlinear differential equations // Ukr. Mat. Zh. - 1962. - 14, № 1. - pp. 57-68.

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