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Abstract <p>Periodic solutions of impulsive system of differential equations with a nonlinear function under the sign of the second-order differential and with maxima are investigated. The problem is reduced to a system of nonlinear functional integral equations in the Banach space <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12202_2025_8188_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="107" /> </InlineMediaObject> <EquationSource Format="TEX">\(BD\left([0,T],\mathbb{R}^{n}\right)\)</EquationSource> <!--LobJMat2560025Fayziyev-m1--> </InlineEquation>. The method of successive approximations in combination with the method of contracting mappings proves the existence and uniqueness of a periodic solution of nonlinear system of functional integral equations with maxima. The practical search for periodic solutions is reduced to calculating the index of an isolated point, i.e., to calculating the rotation of homotopic vector fields.</p>

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Periodic Solutions of Impulsive System of Equations with a Nonlinear Function Under the Sign of a Second-Order Differential and Maxima

  • 期刊论文

  • 发表日期：

    2025年2月1日

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  • A. K. Fayziyev,
  • T. K. Yuldashev

摘要

Abstract

Periodic solutions of impulsive system of differential equations with a nonlinear function under the sign of the second-order differential and with maxima are investigated. The problem is reduced to a system of nonlinear functional integral equations in the Banach space \(BD\left([0,T],\mathbb{R}^{n}\right)\) . The method of successive approximations in combination with the method of contracting mappings proves the existence and uniqueness of a periodic solution of nonlinear system of functional integral equations with maxima. The practical search for periodic solutions is reduced to calculating the index of an isolated point, i.e., to calculating the rotation of homotopic vector fields.