Three positive solutions for a nonlinear nth-order m-point boundary value problem

被引：23

作者：

Guo, Yanping ^{[1
]}

Ji, Yude ^{[1
]}

Zhang, Jiehua ^{[1
]}

机构：

[1] Hebei Univ Sci & Technol, Coll Sci, Shijiazhuang 050018, Hebei, 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：

Green's function; Leggett-Williams fixed point theorem; positive solution;

D O I：

10.1016/j.na.2007.03.041

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we consider the existence of at least three positive solutions for the nonlinear nth-order in-point boundary value problem u((n))(t) + f(t, u) = 0, t is an element of (0, 1), u(0) = 0, u' (0)= ... =u((n-2)) (0) = 0, u(1) (m-2)Sigma(i=1) k(i)u(xi(i)), where u > 2, k(i) > 0 (i = 1, 2, ..., m-2), 0 < xi(1) < xi(2) < ... < xi(m-2) < 1. The associated Green's function for the nth-order in-point boundary value problem is first given, and growth conditions are imposed on the nonlinearity f which yield the existence of multiple positive solutions by using the Leggett-Williams fixed point theorem. (C) 2007 Elsevier Ltd. All rights reserved.

引用

页码：3485 / 3492

页数：8

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