Averaging of a Normal System of Ordinary Differential Equations of High Frequency with a Multipoint Boundary Value Problem on a Semiaxis

IF 0.5 Q3 MATHEMATICS

Russian Mathematics Pub Date : 2024-06-25 DOI:10.3103/s1066369x2470018x

V. B. Levenshtam

引用次数: 0

Abstract

A multipoint boundary value problem for a nonlinear normal system of ordinary differential equations with a rapidly time-oscillating right-hand side is considered on a positive time semiaxis. For this problem, which depends on a large parameter (high oscillation frequency), a limiting (averaged) multipoint boundary value problem is constructed and a limiting transition in the Hölder space of bounded vector functions defined on the considered semiaxis is justified. Thus, for normal systems of differential equations in the case of a multipoint boundary value problem, the Krylov–Bogolyubov averaging method on the semiaxis is justified.

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带有半轴上多点边界值问题的高频常微分方程常态系统的平均化

摘要在正时间半轴上考虑了具有快速时间振荡右边的非线性正态常微分方程系统的多点边界值问题。对于这个依赖于一个大参数（高振荡频率）的问题，构造了一个极限（平均）多点边界值问题，并证明了在所考虑的半轴上定义的有界向量函数的赫尔德空间中的极限转换。因此，对于正常微分方程系统的多点边界值问题，半轴上的 Krylov-Bogolyubov 平均法是合理的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Russian Mathematics MATHEMATICS-

CiteScore

0.90

自引率

25.00%

发文量

期刊介绍： Russian Mathematics is a peer reviewed periodical that encompasses the most significant research in both pure and applied mathematics.