publication . Article . 2010

The upper and lower solution method for nonlinear third-order three-point boundary value problem ∗

Jian-Ping Sun; Qiu-Yan Ren; Ya-Hong Zhao;

Open Access English

Published: 01 May 2010 Journal: Electronic Journal of Qualitative Theory of Differential Equations (issn: 1417-3875, eissn: 1417-3875,

Publisher: University of Szeged

Summary

Abstract

This paper is concerned with the following nonlinear third-order three-point boundary value problem \[\left\{ \begin{array}{l} u^{\prime \prime \prime }(t)+f\left( t,u\left( t\right) ,u^{\prime}\left(t\right) \right) =0,\, t\in \left[ 0,1\right], \\ u\left( 0\right) =u^{\prime }\left( 0\right) =0,\, u^{\prime}\left( 1\right) =\alpha u^{\prime }\left( \eta \right),\label{1.1} \end{array} \right.\] where $0<\eta <1$ and $0\leq \alpha <1.$ A new maximum principle is established and some existence criteria are obtained for the above problem by using the upper and lower solution method.

doi: 10.14232/ejqtde.2010.1.26

Subjects

free text keywords: Mathematics, QA1-939, Nonlinear system, Boundary value problem, Maximum principle, Mathematical optimization, Third order

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