Positive solutions of the three-point boundary value problem for second order differential equations with an advanced argument

被引：40

作者：

Yang, Chen ^{[1
]}

Zhai, Chengbo ^{[1
]}

Yan, Jurang ^{[1
]}

机构：

[1] Shanxi Univ, Dept Math, Taiyuan 030006, Shanxi, Peoples R China

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2006年 / 65卷 / 10期

关键词：

three-point boundary value problem; fixed point index; cone; positive solution;

D O I：

10.1016/j.na.2005.11.003

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, by using the fixed point index method, we establish the existence of at least one or at least two positive solutions to the three-point boundary value problem for a second order differential equation with an advanced argument u" (t) + a (t) f (u (h (t))) = 0, t epsilon (0, 1), u(0) = 0, alpha u(q) = u(1), where eta epsilon (0, 1), alpha > 0, and 1 - alpha eta > 0. As an application, we also give an example to demonstrate our result. (c) 2005 Elsevier Ltd. All rights reserved.

引用

页码：2013 / 2023

页数：11

共 14 条

[1] FIXED-POINT EQUATIONS AND NONLINEAR EIGENVALUE PROBLEMS IN ORDERED BANACH-SPACES
AMANN, H
[J]. SIAM REVIEW, 1976, 18 (04) : 620 - 709
[2] Multiple positive solutions for a three-point boundary value problem
Anderson, D
[J]. MATHEMATICAL AND COMPUTER MODELLING, 1998, 27 (06) : 49 - 57
[3] Dajun G., 1988, NONLINEAR PROBLEMS A
[4] Deimling K., 2010, NONLINEAR FUNCTIONAL, DOI DOI 10.1007/978-3-662-00547-7
[5] Solvability of three point boundary value problems at resonance
Feng, W
Webb, JRL
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1997, 30 (06) : 3227 - 3238
[6] A sharper condition for the solvability of a three-point second order boundary value problem
Gupta, CP
Trofimchuk, SI
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1997, 205 (02) : 586 - 597
[7] SOLVABILITY OF A 3-POINT NONLINEAR BOUNDARY-VALUE PROBLEM FOR A 2ND-ORDER ORDINARY DIFFERENTIAL-EQUATION
GUPTA, CP
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1992, 168 (02) : 540 - 551
[8] Positive solutions of a nonlinear three-point boundary value problem
Liu, B
[J]. APPLIED MATHEMATICS AND COMPUTATION, 2002, 132 (01) : 11 - 28
[9] Ma R, 1998, APPL MATH LETT, V34, P1
[10] Multiplicity of positive solutions for second-order three-point boundary value problems
Ma, RY
[J]. COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2000, 40 (2-3) : 193 - 204

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