Bifurcation from interval and positive solutions for a class of fourth-order two-point boundary value problem

被引：15

作者：

Shen, Wenguo ^{[1
]}

He, Tao ^{[1
]}

机构：

[1] Lanzhou Inst Technol, Dept Basic Courses, Lanzhou 730050, Peoples R China

来源：

BOUNDARY VALUE PROBLEMS | 2013年

关键词：

topological degree; fourth-order ordinary differential equation; bifurcation; positive solution; eigenvalue; NODAL SOLUTIONS; EIGENVALUE PROBLEMS; EQUATIONS;

D O I：

10.1186/1687-2770-2013-170

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the fourth-order two-point boundary value problem x'''' + kx '' + lx = f(t, x), 0 < t < 1, x(0) = x(1) = x'(0) = x'(1) = 0, which is not necessarily linearizable. We give conditions on the parameters k, l and f(t, x) that guarantee the existence of positive solutions. The proof of our main result is based upon topological degree theory and global bifurcation techniques.

引用

页数：12

共 50 条

[1] 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
[2] Positive solutions to a singular fourth-order two-point boundary value problem
Yao, Qingliu
[J]. ANNALES POLONICI MATHEMATICI, 2011, 100 (01) : 1 - 12
[3] Triple positive solutions of a class of fourth-order two-point boundary value problems
Yang, Yun-Rui
[J]. APPLIED MATHEMATICS LETTERS, 2010, 23 (04) : 366 - 370
[4] Bifurcation from interval and positive solutions of a nonlinear fourth-order boundary value problem
Ma, Ruyun
Xu, Jia
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2010, 72 (01) : 113 - 122
[5] POSITIVE SOLUTIONS OF FOURTH-ORDER TWO-POINT BOUNDARY VALUE PROBLEMS
马如云
[J]. Annals of Applied Mathematics, 1999, (03) : 305 - 313
[6] Nodal solutions for a fourth-order two-point boundary value problem
Ma, RY
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2006, 314 (01) : 254 - 265
[7] EXISTENCE AND UNIQUENESS OF POSITIVE SOLUTIONS TO A FOURTH-ORDER TWO-POINT BOUNDARY-VALUE PROBLEM
Jleli, Mohamed
Samet, Bessem
[J]. ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 2013,
[8] POSITIVE SOLUTIONS FOR SEMIPOSITONE FOURTH-ORDER TWO-POINT BOUNDARY VALUE PROBLEMS
Yang, Dandan
Zhu, Hongbo
Bai, Chuanzhi
[J]. ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 2007,
[9] Nodal Solutions for a Class of Fourth-Order Two-Point Boundary Value Problems
Xu, Jia
Han, XiaoLing
[J]. BOUNDARY VALUE PROBLEMS, 2010,
[10] Nodal Solutions for a Class of Fourth-Order Two-Point Boundary Value Problems
Jia Xu
XiaoLing Han
[J]. Boundary Value Problems, 2010

← 1 2 3 4 5 →