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Abstract <p> The paper considers a system of ordinary differential equations with nonlinear boundary conditions in the form of equalities and inequalities. For this problem, sufficient conditions for the existence of solutions on a certain family of closed intervals are obtained. In the particular case of the Cauchy problem, these conditions turn into the classical conditions of the Peano and Carathéodory theorems. Some examples are given that illustrate the main result. </p>

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Generalization of Peano and Carathéodory Theorems for a Boundary Value Problem

  • 期刊论文

  • 发表日期：

    2025年2月1日

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  • E. R. Avakov,
  • G. G. Magaril-Il’yaev

摘要

Abstract

The paper considers a system of ordinary differential equations with nonlinear boundary conditions in the form of equalities and inequalities. For this problem, sufficient conditions for the existence of solutions on a certain family of closed intervals are obtained. In the particular case of the Cauchy problem, these conditions turn into the classical conditions of the Peano and Carathéodory theorems. Some examples are given that illustrate the main result.