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

页码：2185 / 2192

页数：8

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