Positive solutions of fourth-order nonlinear singular boundary value problems

被引：6

作者：

Xu, Fuyi ^{[1
]}

Su, Hua ^{[2
]}

Zhang, Xiaoyan ^{[2
]}

机构：

[1] Shandong Univ Technol, Sch Math & Informat Sci, Zibo 255049, Peoples R China

[2] Shandong Univ, Sch Math & Syst Sci, Jinan 250100, Peoples R China

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2008年 / 68卷 / 05期

基金：

中国国家自然科学基金;

关键词：

fourth-order singular differential equation; cone; positive solutions; fixed point theory;

D O I：

10.1016/j.na.2006.12.021

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the existence of positive solutions for the following fourth-order singular Sturm-Liouville boundary value problem: [GRAPHICS] where g, p may be singular at t = 0 and/or 1. Moreover F(t, x) may also have singularity at x = 0. The existence and multiplicity theorems of positive solutions for the fourth-order singular Sturm-Liouville boundary value problem are obtained by using the first eigenvalue of the corresponding linear problems. Our results significantly extend and improve many known results including singular and nonsingular cases. (c) 2007 Elsevier Ltd. All rights reserved.

引用

页码：1284 / 1297

页数：14

共 50 条

[31] Existence of positive solutions of a nonlinear fourth-order boundary value problem
Ma, Ruyun
Xu, Ling
APPLIED MATHEMATICS LETTERS, 2010, 23 (05) : 537 - 543
[32] Uniqueness of Positive Solutions for a Class of Fourth-Order Boundary Value Problems
Caballero, J.
Harjani, J.
Sadarangani, K.
ABSTRACT AND APPLIED ANALYSIS, 2011,
[33] Existence of positive solutions for the fourth-order elliptic boundary value problems
Li, Yongxiang
Yang, Shengbin
BOUNDARY VALUE PROBLEMS, 2025, 2025 (01):
[34] Nonresonant singular fourth-order boundary value problems
Jiang, DQ
Liu, HZ
Xu, XJ
APPLIED MATHEMATICS LETTERS, 2005, 18 (01) : 69 - 75
[35] Positive solutions of fourth-order boundary value problems with two parameters
Li, YX
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2003, 281 (02) : 477 - 484
[36] Positive Solutions for a Singular Superlinear Fourth-Order Equation with Nonlinear Boundary Conditions
Yan, Dongliang
JOURNAL OF FUNCTION SPACES, 2020, 2020
[37] Positive solutions of fourth-order two point boundary value problems
Liu, B
APPLIED MATHEMATICS AND COMPUTATION, 2004, 148 (02) : 407 - 420
[38] Multiple Solutions for a Class of Nonlinear Fourth-Order Boundary Value Problems
Lin, Longfei
Liu, Yansheng
Zhao, Daliang
SYMMETRY-BASEL, 2020, 12 (12): : 1 - 13
[39] Nonzero Solutions for Nonlinear Systems of Fourth-Order Boundary Value Problems
Agarwal, Ravi P.
Jleli, Mohamed
Samet, Bessem
JOURNAL OF MATHEMATICS, 2021, 2021
[40] NODAL SOLUTIONS OF SOME NONLINEAR FOURTH-ORDER BOUNDARY VALUE PROBLEMS
Aliyeva, Yagut N.
PROCEEDINGS OF THE INSTITUTE OF MATHEMATICS AND MECHANICS, 2024, 50 (01): : 104 - 114

← 1 2 3 4 5 →