Global bifurcation on time scales

被引：25

作者：

Davidson, FA ^{[1
]}

Rynne, BP

机构：

[1] Univ Dundee, Dept Math, Dundee DD1 4HN, Scotland

[2] Heriot Watt Univ, Dept Math, Edinburgh EH14 4AS, Midlothian, Scotland

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2002年 / 267卷 / 01期

关键词：

Sturm-Liouville; time scale; global bifurcation;

D O I：

10.1006/jmaa.2001.7780

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the structure of the solution set of a nonlinear Sturm-Liouville boundary value problem defined on a general time scale. Using global bifurcation theory we show that unbounded continua of nontrivial solutions bifurcate from the trivial solution at the eigenvalues of the linearization, and we show that certain nodal properties of the solutions are preserved along these continua. These results extend the well-known results of Rabinowitz for the case of Sturm-Liouville ordinary differential equations. (C) 2002 Elsevier Science (USA).

引用

页码：345 / 360

页数：16

共 10 条

[1] Sturm-Liouville eigenvalue problems on time scales [J].