Successive Iteration and Positive Solutions for A \(p\)-Laplacian Multipoint Boundary Value Problem

Abstract

In this paper, we study the existence of positive solutions for the one-dimensional p-Laplacian differential equation, \((\phi_{p}(u^{\prime}(t)))^{\prime}+q(t)f(t,u(t),u^{\prime}(t))=0\) \(t\in(0,1),\) subject to the following Multipoint Boundary condition, \(u'(0)=\sum_{i=1}^{n}\alpha_{i}u'(\xi_{i})\), \(u(1)=\sum_{i=1}^{n}\beta_{i}u(\xi_{i}),\) by applying a monotone iterative method. doi:10.1017/S1446181108000205