Positive solutions of m-point boundary value problems

被引：108

作者：

Zhang, GW ^{[1
]}

Sun, JX

机构：

[1] Northeastern Univ, Dept Math, Shenyang 110006, Liaoning, Peoples R China

[2] Xuzhou Normal Univ, Dept Math, Xuzhou 221116, Jiangsu, Peoples R China

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2004年 / 291卷 / 02期

基金：

中国国家自然科学基金;

关键词：

second-order singular equation; multi-point boundary value problem; positive solution; cone; fixed point index;

D O I：

10.1016/j.jmaa.2003.11.034

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The second-order m-point boundary value problem { phi" (x) + h (x) f (phi(x)) = 0, 0 < x < 1, phi(0) = 0, phi(1) = Sigma(i=1)(m-2) a(i)phi(xi(i)), is considered under some conditions concerning the first eigenvalue of the relevant linear operator, where xi(i) epsilon (0, 1) with 0 < xi(1) < xi(2) < (...) < xi(m-2) < 1, a(i) epsilon [0, infinity) with Sigma(i=1)(m-2) a(i) < 1. h (x) is allowed to be singular at x = 0 and x = 1. The existence of positive solutions and multiple positive solutions is obtained by means of fixed point index theory. Similarly conclusions hold for some other m-point boundary value conditions. (C) 2003 Elsevier Inc. All rights reserved.

引用

页码：406 / 418

页数：13

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