Generalization of Peano and Carathéodory theorems for a boundary value problem

E. R. Avakov^a, G. G. Magaril-Il'yaev<sup>bcd

a</sup> V. A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences, Moscow
^b Lomonosov Moscow State University
^c Institute for Information Transmission Problems of the Russian Academy of Sciences (Kharkevich Institute), Moscow
^d Southern Mathematical Institute of the Vladikavkaz Scientific Center of the Russian Academy of Sciences, Vladikavkaz

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.

Keywords: differential equation, boundary conditions, Schauder theorem.

UDC: 517.927.4

Received: 21.07.2024

DOI: 10.4213/mzm14450

 English version: Mathematical Notes, 2025, 117:2, 173–180

Bibliographic databases:

• 
•