Global bifurcation and multiple results for Sturm-Liouville problems

被引：16
|
作者：
Cui, Yujun [1 ]
Sun, Jingxian [2 ]
Zou, Yumei [1 ]
机构：
[1] Shandong Univ Sci & technol, Dept Appl Math, Qingdao 266510, Peoples R China
[2] Xuzhou Normal Univ, Dept Math, Xuzhou 221116, Peoples R China
来源：
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2011年 / 235卷 / 08期
基金：
美国国家科学基金会;
关键词：
Global bifurcation; Sturm-Liouville problems; BOUNDARY-VALUE-PROBLEMS; NONLINEAR EIGENVALUE PROBLEMS; POSITIVE SOLUTIONS; EXISTENCE; EQUATIONS;
D O I：
10.1016/j.cam.2010.10.014
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We consider the nonlinear Sturm-Liouville boundary value problem {(Lu)(t) = lambda a(t)f(u(t)), 0 < t < 1, R-i(u)= alpha(i)u(0) + beta(1)u'(0) = 0, R-2(u) = alpha(2)u(1) + beta(2)u'(1) = 0, where L is the linear Sturm-Liouville operator (Lu)(t) = -(p(t)u' (t))' + q(t)u(t). We obtain a global bifurcation result for a related bifurcation problem. We then use this to obtain multiple (at least eight) solutions of the Sturm-Liouville problem having specified nodal properties. (C) 2010 Elsevier B.V. All rights reserved.
引用
收藏
页码：2185 / 2192
页数：8
相关论文
共 50 条
  • [31] Discrete fourth-order Sturm-Liouville problems
    Ben-Artzi, Matania
    Croisille, Jean-Pierre
    Fishelov, Dalia
    Katzir, Ron
    IMA JOURNAL OF NUMERICAL ANALYSIS, 2018, 38 (03) : 1485 - 1522
  • [32] Sturm-Liouville problems and global bounds by small control sets and applications to quantum graphs
    Egidi, Michela
    Mugnolo, Delio
    Seelmann, Albrecht
    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2024, 535 (01)
  • [33] On the number of solutions of two classes of Sturm-Liouville boundary value problems
    Benmezai, Abdelhamid
    NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2009, 70 (04) : 1504 - 1519
  • [34] Multiple Solutions for Second-Order Sturm-Liouville Boundary Value Problems with Subquadratic Potentials at Zero
    Liu, Dan
    Zhang, Xuejun
    Song, Mingliang
    JOURNAL OF MATHEMATICS, 2021, 2021
  • [35] Multiple Positive Solutions of Singular Nonlinear Sturm-Liouville Problems with Caratheodory Perturbed Term
    Han, Yuefeng
    Zhang, Xinguang
    Liu, Lishan
    Wu, Yonghong
    JOURNAL OF APPLIED MATHEMATICS, 2012,
  • [36] Sturm-Liouville BVP in Banach space
    Su, Hua
    Liu, Lishan
    Wang, Xinjun
    ADVANCES IN DIFFERENCE EQUATIONS, 2011, : 1 - 12
  • [37] BIFURCATION IN NONLINEAR STURM-LIOUVILLE PROBLEMS WITH INDEFINITE WEIGHT AND SPECTRAL PARAMETER IN THE BOUNDARY CONDITION
    Gurbanova, Ulkar, V
    PROCEEDINGS OF THE INSTITUTE OF MATHEMATICS AND MECHANICS, 2021, 47 (01): : 46 - 54
  • [38] New results of positive solutions for the Sturm-Liouville problem
    GC Yang
    HB Feng
    Boundary Value Problems, 2016
  • [39] Spectral functions for regular Sturm-Liouville problems
    Fucci, Guglielmo
    Graham, Curtis
    Kirsten, Klaus
    JOURNAL OF MATHEMATICAL PHYSICS, 2015, 56 (04)
  • [40] Computation of the eigenelements of singular Sturm-Liouville problems
    El-Gebeily, MA
    INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, 2001, 78 (04) : 539 - 550
12345