Existence and Uniqueness of Solutions for the First Order Non-linear Differential Equations with Multi-point Boundary Conditions

M.J. Mardanov, Y.A. Sharifov, Humbet Aliyev, R.A. Sardarova

Abstract

This article discusses the existence and uniqueness of solutions for the system of non-linear first order ordinary differential equations with multipoint boundary conditions. The Green function is constructed, and the problem is reduced to the equivalent integral equation. Existence and uniqueness of the solution to this problem is studied using the Banach contraction mapping principle and Schaefer’s fixed point theorem.

Keywords

Multipoint boundary conditions, existence and uniqueness solutions, fixed point theorems, first order differential equation, Schaefer's fixed point theorem.

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