Boundary value problems for a class of first order quasilinear ordinary differential equations

Abstract

Using continuation theorems of Leray-Schauder degree theory, we obtain existence results for the first order quasilinear boundary value problem

where $\varphi :\mathbb{R}\to (-a,a)$ is an homeomorphism such that $\varphi (0)=0$ and $f:[0,T]\times \mathbb{R}\to \mathbb{R}$ is a continuous function, $a$ and $T$ being positive real numbers and $b$ some non zero real number.