Bifurcation from interval and positive solutions of a nonlinear fourth-order boundary value problem

被引：34

作者：

Ma, Ruyun ^{[1
]}

Xu, Jia ^{[1
]}

机构：

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

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2010年 / 72卷 / 01期

关键词：

Krein-Rutman theorem; Topological degree; Fourth-order ordinary differential equations; Bifurcation; Positive solutions; Eigenvalue; STURM-LIOUVILLE PROBLEMS; NODAL SOLUTIONS; BEAM EQUATIONS; EXISTENCE; MULTIPLICITY; UNIQUENESS;

D O I：

10.1016/j.na.2009.06.061

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 of the nonlinear boundary value problem u((4))(t) = f(t, u(t), u ''(t)), t is an element of (0, 1), u(0) = u(1) = u ''(0) = u ''(1) = 0, which is not necessarily linearizable. Our approaches are based on Krein-Rutman theorem, topological degree theory and global bifurcation techniques. (C) 2009 Elsevier Ltd. All rights reserved.

引用

页码：113 / 122

页数：10

共 50 条

[1] Bifurcation of positive solutions of a nonlinear discrete fourth-order boundary value problem
Ma, Ruyun
Gao, Chenghua
[J]. ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, 2013, 64 (03): : 493 - 506
[2] Bifurcation of positive solutions of a nonlinear discrete fourth-order boundary value problem
Ruyun Ma
Chenghua Gao
[J]. Zeitschrift für angewandte Mathematik und Physik, 2013, 64 : 493 - 506
[3] Bifurcation from interval and positive solutions for a class of fourth-order two-point boundary value problem
Shen, Wenguo
He, Tao
[J]. BOUNDARY VALUE PROBLEMS, 2013,
[4] Bifurcation from interval and positive solutions for a class of fourth-order two-point boundary value problem
Wenguo Shen
Tao He
[J]. Boundary Value Problems, 2013
[5] Bifurcation and positive solutions of a nonlinear fourth-order dynamic boundary value problem on time scales
Hua Luo
[J]. Advances in Difference Equations, 2013
[6] Bifurcation and positive solutions of a nonlinear fourth-order dynamic boundary value problem on time scales
Luo, Hua
[J]. ADVANCES IN DIFFERENCE EQUATIONS, 2013,
[7] Existence of positive solutions of a nonlinear fourth-order boundary value problem
Ma, Ruyun
Xu, Ling
[J]. APPLIED MATHEMATICS LETTERS, 2010, 23 (05) : 537 - 543
[8] Positive Solutions for a Fourth-Order Boundary Value Problem
Wang, Kun
Yang, Zhilin
[J]. JOURNAL OF MATHEMATICS, 2013, 2013
[9] Existence and uniqueness of positive solutions for a nonlinear fourth-order boundary value problem
Harjani, J.
Sadarangani, K.
[J]. POSITIVITY, 2010, 14 (04) : 849 - 858
[10] Existence and uniqueness of positive solutions for a nonlinear fourth-order boundary value problem
J. Harjani
K. Sadarangani
[J]. Positivity, 2010, 14 : 849 - 858

← 1 2 3 4 5 →