Spectral properties of non-local differential operators

    Research output: Contribution to journalArticlepeer-review

    7 Citations (Scopus)

    Abstract

    In this article we consider the spectral properties of a class of non-local operators that arise from the study of non-local reaction-diffusion equations. Such equations are used to model a variety of physical and biological systems with examples ranging from Ohmic heating to population dynamics. The operators studied here are bounded perturbations of linear (local) differential operators. The non-local perturbation is in the form of an integral term. It is shown here that the spectral properties of these non-local operators can differ considerably from those of their local counterpart. Multiplicities of eigenvalues are studied and new oscillation results for the associated eigenfunctions are presented. These results highlight problems with certain similar results and provide an alternative formulation. Finally, the stability of steady states of associated non-local reaction-diffusion equations is discussed.
    Original languageEnglish
    Pages (from-to)717-734
    Number of pages18
    JournalApplicable Analysis
    Volume85
    Issue number6-7
    DOIs
    Publication statusPublished - 2006

    Keywords

    • Eigenvalues
    • Multiplicities
    • Eigenfunctions
    • Oscillation theorem

    Fingerprint

    Dive into the research topics of 'Spectral properties of non-local differential operators'. Together they form a unique fingerprint.

    Cite this