Global bifurcation on time scales

Fordyce A. Davidson, Bryan P. Rynne

Research output: Contribution to journalArticle

18 Citations (Scopus)

Abstract

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. © 2002 Elsevier Science (USA).

Original languageEnglish
Pages (from-to)345-360
Number of pages16
JournalJournal of Mathematical Analysis and Applications
Volume267
Issue number1
DOIs
Publication statusPublished - 1 Mar 2002

Keywords

  • Global bifurcation
  • Sturm-Liouville
  • Time scale

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