2017
Том 69
№ 9

All Issues

On Certain Properties of the Solutions of Systems of Nonlinear Differential Equations with Slowly Varying Parameters

Lykova O. B.

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Abstract

In a previous paper the author proposed an algorithm for finding an approximate (with precision up to a magnitude of order e) two-parameter family of special solutions of the system. In this paper the existence and uniqueness ot a corresponding exact two-parameter family of solutions of system (1) is proved; the difference between the exact family of solutions and its mth approximation is shown to be of the order of em; the property of attraction to the found approximate family of solutions is established for any solutions of system (1) having initial values which belong to the region of definition of the exact two-parameter family of solutions of system (1)

Citation Example: Lykova O. B. On Certain Properties of the Solutions of Systems of Nonlinear Differential Equations with Slowly Varying Parameters // Ukr. Mat. Zh. - 1960. - 12, № 3. - pp. 267 - 278.

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