Dead Core Problems for Singular Equations with http://static-content.springer.com/image/art%3A10.1155%2F2007%2F18961/MediaObjects/13661_2007_Article_636_IEq1_HTML.gif -Laplacian

  • Ravi P Agarwal1Email author,

    Affiliated with

    • Donal O'Regan2 and

      Affiliated with

      • Svatoslav Staněk3

        Affiliated with

        Boundary Value Problems20072007:018961

        DOI: 10.1155/2007/18961

        Received: 27 May 2007

        Accepted: 6 September 2007

        Published: 16 December 2007

        Abstract

        The paper discusses the existence of positive solutions, dead core solutions, and pseudo dead core solutions of the singular problem http://static-content.springer.com/image/art%3A10.1155%2F2007%2F18961/MediaObjects/13661_2007_Article_636_IEq2_HTML.gif , http://static-content.springer.com/image/art%3A10.1155%2F2007%2F18961/MediaObjects/13661_2007_Article_636_IEq3_HTML.gif , http://static-content.springer.com/image/art%3A10.1155%2F2007%2F18961/MediaObjects/13661_2007_Article_636_IEq4_HTML.gif . Here http://static-content.springer.com/image/art%3A10.1155%2F2007%2F18961/MediaObjects/13661_2007_Article_636_IEq5_HTML.gif is a positive parameter, http://static-content.springer.com/image/art%3A10.1155%2F2007%2F18961/MediaObjects/13661_2007_Article_636_IEq6_HTML.gif , http://static-content.springer.com/image/art%3A10.1155%2F2007%2F18961/MediaObjects/13661_2007_Article_636_IEq7_HTML.gif , http://static-content.springer.com/image/art%3A10.1155%2F2007%2F18961/MediaObjects/13661_2007_Article_636_IEq8_HTML.gif , http://static-content.springer.com/image/art%3A10.1155%2F2007%2F18961/MediaObjects/13661_2007_Article_636_IEq9_HTML.gif may be singular at http://static-content.springer.com/image/art%3A10.1155%2F2007%2F18961/MediaObjects/13661_2007_Article_636_IEq10_HTML.gif and http://static-content.springer.com/image/art%3A10.1155%2F2007%2F18961/MediaObjects/13661_2007_Article_636_IEq11_HTML.gif is singular at http://static-content.springer.com/image/art%3A10.1155%2F2007%2F18961/MediaObjects/13661_2007_Article_636_IEq12_HTML.gif .

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        Authors’ Affiliations

        (1)
        Department of Mathematical Sciences, Florida Institute of Technology
        (2)
        Department of Mathematics, National University of Ireland
        (3)
        Department of Mathematical Analysis, Faculty of Science, Palacký University

        References

        1. Baxley JV, Gersdorff GS: Singular reaction-diffusion boundary value problems. Journal of Differential Equations 1995,115(2):441–457. 10.1006/jdeq.1995.1022MATHMathSciNetView Article
        2. Bobisud LE: Behavior of solutions for a Robin problem. Journal of Differential Equations 1990,85(1):91–104. 10.1016/0022-0396(90)90090-CMATHMathSciNetView Article
        3. Agarwal RP, O'Regan D, Staněk S: Dead cores of singular Dirichlet boundary value problems with-Laplacian. in preparation
        4. Cabada A, Pouso RL: Existence results for the problem http://static-content.springer.com/image/art%3A10.1155%2F2007%2F18961/MediaObjects/13661_2007_Article_636_IEq14_HTML.gif with nonlinear boundary conditions. Nonlinear Analysis: Theory, Methods & Applications 1999,35(2):221–231. 10.1016/S0362-546X(98)00009-1MATHMathSciNetView Article

        Copyright

        © Ravi P. Agarwal et al. 2007

        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.