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<p>An overview of some results of the theory of the averaging method associated with the names of N.&#xa0;M.&#xa0;Krylov and N.&#xa0;N.&#xa0;Bogolyubov for normal systems of ordinary differential equations with initial data (Cauchy problem) on a&#xa0;finite time interval is presented. Systems of ODES with high-frequency terms are considered, among which may be proportional to certain positive degrees of high frequency.</p>

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AVERAGING METHOD FOR ORDINARY DIFFERENTIAL EQUATIONS WITH LARGE HIGH-FREQUENCY TERMS. I

  • 期刊论文

  • 发表日期：

    2025年8月1日

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  • V. B. Levenshtam

摘要

An overview of some results of the theory of the averaging method associated with the names of N. M. Krylov and N. N. Bogolyubov for normal systems of ordinary differential equations with initial data (Cauchy problem) on a finite time interval is presented. Systems of ODES with high-frequency terms are considered, among which may be proportional to certain positive degrees of high frequency.