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

Bo Sun

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



DOI: http://dx.doi.org/10.21914/anziamj.v49i0.255



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ANZIAM Journal, ISSN 1446-8735, copyright Australian Mathematical Society.