Positive solutions for a four-point boundary value problem with the p-Laplacian

被引：22

作者：

Lian, Hairong ^{[1
,2
]}

Ge, Weigao ^{[1
]}

机构：

[1] Beijing Inst Technol, Dept Math, Beijing 100081, Peoples R China

[2] China Univ Geosci, Sch Informat Engn, Beijing 100083, Peoples R China

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2008年 / 68卷 / 11期

基金：

中国国家自然科学基金;

关键词：

multi-point boundary value problem; positive solution; fixed point theorem; cone;

D O I：

10.1016/j.na.2007.03.042

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we study the nonlinear four-point boundary value problem with the p-Laplacian (phi(p)(u'))'+f(t,u(t))=0, 0 < t < 1, u(0)-alpha u'(xi) = 0, u(1) + beta u' (eta) = 0, where phi(p)(S) = |S|(p-2)s, P > 1, alpha, beta > 0, 0 < xi < eta < 1. By applying a fixed point theorem in cones, sufficient conditions are given for the existence of a positive solution and multiple positive solutions. The interesting point is the Sturm-Liouville-like boundary condition, which was rarely treated until now. (C) 2007 Elsevier Ltd. All rights reserved.

引用

页码：3493 / 3503

页数：11

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