Existence of positive solutions due to non-local interactions in a class of nonlinear boundary value problems

    Research output: Contribution to journalArticlepeer-review

    Abstract

    We consider a class of non-local boundary value problems of the type used to model a variety of physical and biological processes, from Ohmic heating to population dynamics. Of particular relevance therefore is the existence of positive solutions. We are interested in the existence of such solutions that arise as a direct consequence of the non-local interactions in the problem. Conditions are therefore imposed that preclude the existence of a positive solution for the related local problem. Under these conditions, we prove that there exists a unique positive solution to the boundary value problem for all sufficiently strong non-local interactions and no positive solutions exist otherwise.
    Original languageEnglish
    Pages (from-to)15-28
    Number of pages14
    JournalMethods and Applications of Analysis
    Volume14
    Issue number1
    Publication statusPublished - 2007

    Keywords

    • Positive solution
    • Boundary value problems

    Fingerprint Dive into the research topics of 'Existence of positive solutions due to non-local interactions in a class of nonlinear boundary value problems'. Together they form a unique fingerprint.

    Cite this