Existence and Uniqueness of Positive Solution for a Singular Nonlinear Second-Order http://static-content.springer.com/image/art%3A10.1155%2F2010%2F254928/MediaObjects/13661_2009_Article_908_IEq1_HTML.gif -Point Boundary Value Problem

  • Xuezhe Lv1 and

    Affiliated with

    • Minghe Pei1Email author

      Affiliated with

      Boundary Value Problems20102010:254928

      DOI: 10.1155/2010/254928

      Received: 25 November 2009

      Accepted: 10 March 2010

      Published: 31 March 2010

      Abstract

      The existence and uniqueness of positive solution is obtained for the singular second-order http://static-content.springer.com/image/art%3A10.1155%2F2010%2F254928/MediaObjects/13661_2009_Article_908_IEq2_HTML.gif -point boundary value problem http://static-content.springer.com/image/art%3A10.1155%2F2010%2F254928/MediaObjects/13661_2009_Article_908_IEq3_HTML.gif for http://static-content.springer.com/image/art%3A10.1155%2F2010%2F254928/MediaObjects/13661_2009_Article_908_IEq4_HTML.gif , http://static-content.springer.com/image/art%3A10.1155%2F2010%2F254928/MediaObjects/13661_2009_Article_908_IEq5_HTML.gif , http://static-content.springer.com/image/art%3A10.1155%2F2010%2F254928/MediaObjects/13661_2009_Article_908_IEq6_HTML.gif , where http://static-content.springer.com/image/art%3A10.1155%2F2010%2F254928/MediaObjects/13661_2009_Article_908_IEq7_HTML.gif , http://static-content.springer.com/image/art%3A10.1155%2F2010%2F254928/MediaObjects/13661_2009_Article_908_IEq8_HTML.gif , http://static-content.springer.com/image/art%3A10.1155%2F2010%2F254928/MediaObjects/13661_2009_Article_908_IEq9_HTML.gif are constants, and http://static-content.springer.com/image/art%3A10.1155%2F2010%2F254928/MediaObjects/13661_2009_Article_908_IEq10_HTML.gif can have singularities for http://static-content.springer.com/image/art%3A10.1155%2F2010%2F254928/MediaObjects/13661_2009_Article_908_IEq11_HTML.gif and/or http://static-content.springer.com/image/art%3A10.1155%2F2010%2F254928/MediaObjects/13661_2009_Article_908_IEq12_HTML.gif and for http://static-content.springer.com/image/art%3A10.1155%2F2010%2F254928/MediaObjects/13661_2009_Article_908_IEq13_HTML.gif . The main tool is the perturbation technique and Schauder fixed point theorem.

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      Authors’ Affiliations

      (1)
      Department of Mathematics, Beihua University

      Copyright

      © X. Lv and M. Pei. 2010

      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.