Existence of three positive solutions for m-point boundary-value problems with one-dimensional p-Laplacian

被引：29

作者：

Feng, Hanying ^{[1
,2
]}

Ge, Weigao ^{[1
]}

机构：

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

[2] Shijiazhuang Mech Engn Coll, Dept Math, Shijiazhuang 050003, Peoples R China

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2008年 / 68卷 / 07期

基金：

中国国家自然科学基金;

关键词：

multipoint boundary value problem; Avery-Peterson's fixed point theorem; positive solution; one-dimensional p-Laplacian;

D O I：

10.1016/j.na.2007.01.029

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we consider the multipoint boundary value problem for the one-dimensional p-Laplacian (phi(p)(u'))' + q(t) f (t, u(t), u'(t)) = 0, t epsilon (0, 1), subject to the boundary conditions: u(0) = 0, u(1) = Sigma(m-2)(i=1) a(i)u(xi(i)), where phi(p)(s) = vertical bar s vertical bar(p-2)s, p > 1,xi(i) epsilon (0, 1) with 0 < xi(1) < xi(2) <... < xi(m-2) 1 and a(i) epsilon [0, 1), 0 <= Sigma(m-2)(i=1) a(i) < 1. Using a fixed point theorem due to Avery and Peterson, we study the existence of at least three positive solutions to the above boundary value problem. The interesting point is that the nonlinear term f explicitly involves a first-order derivative. (c) 2007 Elsevier Ltd. All rights reserved.

引用

页码：2017 / 2026

页数：10

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