Problems with classic homeomorphisms and three-point boundary conditions

TL;DR

This paper investigates the existence of solutions for a boundary value problem involving a homeomorphism and three-point boundary conditions using Leray-Schauder degree theory.

Contribution

It applies Leray-Schauder degree theory to establish solution existence for a specific nonlinear boundary value problem with three-point boundary conditions.

Findings

Existence of at least one solution under given conditions

Application of Leray-Schauder degree theory to nonlinear boundary problems

Analysis of boundary conditions involving homeomorphisms

Abstract

Using Leray-Schauder degree theory we study the existence of at least one solution for the boundary value problem of the type (\varphi(u' ))' = f(t,u,u'), u'(0)=u(0), u'(T)= bu'(0), where \varphi is a homeomorphism such that \varphi(0)=0, f is a continuous function, and T a positive real number and b some non zero real number.