First order systems of odes with nonlinear nonlocal boundary conditions

TL;DR

This paper proves the existence of solutions for a class of first order nonlinear nonlocal boundary value problems using Mawhin's coincidence theory, advancing the mathematical understanding of such systems.

Contribution

It introduces a novel application of Mawhin's coincidence theory to establish solution existence for nonlinear nonlocal boundary conditions.

Findings

Existence of solutions established for the boundary value problem.

Application of Mawhin's coincidence theory to nonlinear nonlocal conditions.

Mathematical framework for analyzing similar systems developed.

Abstract

In this article, we prove an existence of solutions for a non-local boundary value problem with nonlinearity in a nonlocal condition. Our method is based upon the Mawhin's coincidence theory.