Global bifurcation on time scales

Fordyce A. Davidson, Bryan P. Rynne

    Research output: Contribution to journalArticlepeer-review

    19 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.
    Original languageEnglish
    Pages (from-to)345-360
    Number of pages16
    JournalJournal of Mathematical Analysis and Applications
    Volume267
    Issue number1
    DOIs
    Publication statusPublished - 2002

    Keywords

    • Sturm–Liouville
    • Time-scales
    • Global bifurcation

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