An extension of Leggett-Williams norm-type theorem for coincidences and its application

Abstract

In this paper, several versions extension of Leggett-Williams norm-type theorem for coincidences are given and proved to obtain the positive solutions of the operator equation $Mx=Nx$, where $M$ is a quasi-linear operator and $N$ is nonlinear. Moreover, as an application, the existence of positive solutions for multi-point boundary value problem with a $p$-Laplacian is obtained by one of those theorems.