2017
Том 69
№ 7

Всі номери

Некоторые критерии ограниченности решений систем нелинейных дифференциальных уравнений

Скрипник В. П.

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Абстракт

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.

Зразок цитування: Скрипник В. П. Некоторые критерии ограниченности решений систем нелинейных дифференциальных уравнений // Укр. мат. журн. - 1962. - 14, № 1. - С. 57-68.

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