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
收藏
页码：1284 / 1297
页数：14
相关论文
共 50 条
  • [41] Positive solutions of singular boundary value problems for systems of nonlinear fourth order differential equations
    Liu, Lishan
    Kang, Ping
    Wu, Yonghong
    Wiwatanapataphee, Benchawan
    NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2008, 68 (03) : 485 - 498
  • [42] NONTRIVIAL SOLUTIONS OF FOURTH-ORDER SINGULAR BOUNDARY VALUE PROBLEMS WITH SIGN-CHANGING NONLINEAR TERMS
    Zhang, Kemei
    TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS, 2012, 40 (01) : 53 - 70
  • [43] Positive Solutions for a Fourth-Order Boundary Value Problem
    Wang, Kun
    Yang, Zhilin
    JOURNAL OF MATHEMATICS, 2013, 2013
  • [44] Positive solutions for nonlocal fourth-order boundary value problems with all order derivatives
    Yanping Guo
    Fei Yang
    Yongchun Liang
    Boundary Value Problems, 2012
  • [45] Positive solutions for nonlocal fourth-order boundary value problems with all order derivatives
    Guo, Yanping
    Yang, Fei
    Liang, Yongchun
    BOUNDARY VALUE PROBLEMS, 2012,
  • [46] Bifurcation of positive solutions of a nonlinear discrete fourth-order boundary value problem
    Ma, Ruyun
    Gao, Chenghua
    ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, 2013, 64 (03): : 493 - 506
  • [47] Bifurcation of positive solutions of a nonlinear discrete fourth-order boundary value problem
    Ruyun Ma
    Chenghua Gao
    Zeitschrift für angewandte Mathematik und Physik, 2013, 64 : 493 - 506
  • [48] Existence and uniqueness of positive solutions for a nonlinear fourth-order boundary value problem
    Harjani, J.
    Sadarangani, K.
    POSITIVITY, 2010, 14 (04) : 849 - 858
  • [49] Existence and uniqueness of positive solutions for a nonlinear fourth-order boundary value problem
    J. Harjani
    K. Sadarangani
    Positivity, 2010, 14 : 849 - 858
  • [50] Global structure of positive solutions for a fourth-order boundary value problem with singular data
    Ma, Ruyun
    Zhao, Zhongzi
    Ma, Mantang
    ZEITSCHRIFT FUR ANALYSIS UND IHRE ANWENDUNGEN, 2023, 42 (1-2): : 189 - 202
12345