2017
Том 69
№ 9

All Issues

On systems of ordinary differential equations with explicit periodic dependence on the argument

Sharshanov A. A.

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Abstract

The following problem is considered. Given functions $u, v$ are depending on the arguments $x, y, z$ partially differentiate with respect to z and periodic with respect to this argument with a period equal to unity. In addition the functions $u, v$ are analytical in respect to the two other arguments, the Jacobian of these variables is positive with any $z$ for all values of $x, у$ of the region under consideration. Then, we may construct functions $u, v$ satisfying certain conditions depending on $x, y, z, t$, analytical in $x, у$ and differentiable a sufficient number of times with respect to $t$, the Jacobian of these functions in $x, у$ differing from zero for all real values of $z, t$ and the considered $x, y$.

Citation Example: Sharshanov A. A. On systems of ordinary differential equations with explicit periodic dependence on the argument // Ukr. Mat. Zh. - 1962. - 14, № 1. - pp. 68-86.

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