Multiple positive solutions for multipoint boundary value problems with sign changing nonlinearity

被引：19

作者：

Ji, Dehong ^{[1
]}

Feng, Meiqiang ^{[2
]}

Ge, Weigao ^{[1
]}

机构：

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

[2] Beijing Informat Technol, Dept Fundamental Sci, Beijing 100101, Peoples R China

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2008年 / 196卷 / 02期

基金：

中国国家自然科学基金;

关键词：

multiple positive solutions; boundary value problems; fixed point theorem in cones; one-dimensional p-Laplacian;

D O I：

10.1016/j.amc.2007.06.028

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 one-dimensional p-Laplacian (phi(p)(u'))' + q(t)f(t, u) = 0, t is an element of (0, 1), subject to the boundary value conditions: u(0) = (n)Sigma(i=1)alpha(i)u(xi(i)), u(1) = (n)Sigma(i=1)beta(i)u(xi(i)), where phi(p)(s) = vertical bar S vertical bar(p-2)s, P > 1, xi(i) is an element of (0, 1) With 0 < xi(1) < xi(2) < ... < xi(n) < 1 and alpha(i),beta(i) is an element of [0, infinity) satisfy 0 < Sigma(n)(i=1) alpha(i), Sigma(n)(i=1) beta(i) < 1 The nonlinear term f may change sign. Using a fixed point theorem for operators in a cone, we provide sufficient conditions for the existence of multiple positive solutions to the above boundary value problem. (C) 2007 Elsevier Inc. All rights reserved.

引用

页码：511 / 520

页数：10

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