An Approximation Approach to Eigenvalue Intervals for Singular Boundary Value Problems with Sign Changing and Superlinear Nonlinearities

  • Haishen Lü1Email author,

    Affiliated with

    • RaviP Agarwal2, 3 and

      Affiliated with

      • Donal O'Regan4

        Affiliated with

        Boundary Value Problems20092009:103867

        DOI: 10.1155/2009/103867

        Received: 25 June 2009

        Accepted: 5 October 2009

        Published: 26 October 2009

        Abstract

        This paper studies the eigenvalue interval for the singular boundary value problem http://static-content.springer.com/image/art%3A10.1155%2F2009%2F103867/MediaObjects/13661_2009_Article_825_IEq1_HTML.gif , where http://static-content.springer.com/image/art%3A10.1155%2F2009%2F103867/MediaObjects/13661_2009_Article_825_IEq2_HTML.gif may be singular at http://static-content.springer.com/image/art%3A10.1155%2F2009%2F103867/MediaObjects/13661_2009_Article_825_IEq3_HTML.gif ,   http://static-content.springer.com/image/art%3A10.1155%2F2009%2F103867/MediaObjects/13661_2009_Article_825_IEq4_HTML.gif , and may change sign and be superlinear at http://static-content.springer.com/image/art%3A10.1155%2F2009%2F103867/MediaObjects/13661_2009_Article_825_IEq5_HTML.gif . The approach is based on an approximation method together with the theory of upper and lower solutions.

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        Authors’ Affiliations

        (1)
        Department of Applied Mathematics, Hohai University
        (2)
        Department of Mathematical Sciences, Florida Institute of Technology
        (3)
        KFUPM Chair Professor, Mathematics and Statistics Department, King Fahd University of Petroleum and Minerals
        (4)
        Department of Mathematics, National University of Ireland

        Copyright

        © Haishen Lü et al. 2009

        This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.