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Abstract <p> The paper presents a generalization of the classical continuation method for periodic solutions in cases where the implicit function theorem is not applicable. The proposed method relies on geometric considerations and can be used, for example, to prove the existence of forced oscillations in strongly nonlinear oscillator chains. </p>

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On an Approach to Proving the Existence of Forced Oscillations

  • 期刊论文

  • 发表日期：

    2025年9月1日

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  • Ivan Yu. Polekhin

摘要

Abstract

The paper presents a generalization of the classical continuation method for periodic solutions in cases where the implicit function theorem is not applicable. The proposed method relies on geometric considerations and can be used, for example, to prove the existence of forced oscillations in strongly nonlinear oscillator chains.