Existence of solutions of nonlinear m-point boundary-value problems

被引：221

作者：

Ma, RY ^{[1
]}

Castaneda, N

机构：

[1] NW Normal Univ, Dept Matemat, Lanzhou 730070, Gansu, Peoples R China

[2] Cent Connecticut State Univ, Dept Math Sci, New Britain, CT 06050 USA

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2001年 / 256卷 / 02期

基金：

中国国家自然科学基金;

关键词：

ordinary differential equation; existence of solutions; multi-point boundary-value problems; Leray-Schauder continuation theorem;

D O I：

10.1006/jmaa.2000.7320

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the existence of positive solutions to the boundary-value problem u " + a(t)f(u) = 0, t is an element of (0, 1) x'(0)= Sigma (m-2)(i=1) b(i)x'(xi (i)), x(1) = Sigma (m-2)(i=1) a(i)x(xi (i)), where xi (i) is an element of (0, 1) with 0 < <xi>(1) < <xi>(2) < <xi>(m-2) < 1, a(i), b(i) <is an element of> [0, infinity) with 0 < <Sigma>(m-2)(i=1) a(i) < 1, and <Sigma>(m-2)(i=1) b(i) < 1. We show the existence of at least one positive soIution if f is either superlinear or sublinear by applying the fixed point theorem in cones. <(c)> 2001 Academic Press.

引用

页码：556 / 567

页数：12

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