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Abstract <p> For a system of second-order ordinary differential equations with a main positivelyhomogeneous nonlinearity, an a priori estimate of periodic solutions of a fixed period is studied.We find new conditions ensuring the a priori estimate in which the influence of the properties ofthe main nonlinear part, including its set of zeros, is taken into account via upper and lowerfunctional bounds. The satisfiability of the new conditions is analyzed for three types ofnonlinearities.</p>

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A Priori Estimate for Periodic Solutions of a System of Second-Order Ordinary Differential Equations with a Main Positively Homogeneous Nonlinearity

  • 期刊论文

  • 发表日期：

    2025年2月1日

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  • E. Mukhamadiev,
  • A. N. Naimov

摘要

Abstract

For a system of second-order ordinary differential equations with a main positivelyhomogeneous nonlinearity, an a priori estimate of periodic solutions of a fixed period is studied.We find new conditions ensuring the a priori estimate in which the influence of the properties ofthe main nonlinear part, including its set of zeros, is taken into account via upper and lowerfunctional bounds. The satisfiability of the new conditions is analyzed for three types ofnonlinearities.