About the Existence of Solutions of a Boundary Value Problem for a Carathéodory Differential System

Abstract

A boundary value problem of the form $x’=f(t,x),x\in S$ is considered where $f$ is a Carathéodory function and $S$ is a suitable boundary constraint. A related integral equation with an exact number of solutions is studied, in order to show the existence of solutions of the boundary value problem through a fixed point theorem for $w$-maps in the Darbo sense.