Existence of Symmetric Positive Solutions for an http://static-content.springer.com/image/art%3A10.1155%2F2007%2F79090/MediaObjects/13661_2006_Article_665_IEq1_HTML.gif -Point Boundary Value Problem

  • Yongping Sun1Email author and

    Affiliated with

    • Xiaoping Zhang1

      Affiliated with

      Boundary Value Problems20072007:079090

      DOI: 10.1155/2007/79090

      Received: 23 June 2006

      Accepted: 11 March 2007

      Published: 16 May 2007

      Abstract

      We study the second-order http://static-content.springer.com/image/art%3A10.1155%2F2007%2F79090/MediaObjects/13661_2006_Article_665_IEq2_HTML.gif -point boundary value problem http://static-content.springer.com/image/art%3A10.1155%2F2007%2F79090/MediaObjects/13661_2006_Article_665_IEq3_HTML.gif , http://static-content.springer.com/image/art%3A10.1155%2F2007%2F79090/MediaObjects/13661_2006_Article_665_IEq4_HTML.gif , http://static-content.springer.com/image/art%3A10.1155%2F2007%2F79090/MediaObjects/13661_2006_Article_665_IEq5_HTML.gif , where http://static-content.springer.com/image/art%3A10.1155%2F2007%2F79090/MediaObjects/13661_2006_Article_665_IEq6_HTML.gif , http://static-content.springer.com/image/art%3A10.1155%2F2007%2F79090/MediaObjects/13661_2006_Article_665_IEq7_HTML.gif for http://static-content.springer.com/image/art%3A10.1155%2F2007%2F79090/MediaObjects/13661_2006_Article_665_IEq8_HTML.gif with http://static-content.springer.com/image/art%3A10.1155%2F2007%2F79090/MediaObjects/13661_2006_Article_665_IEq9_HTML.gif . http://static-content.springer.com/image/art%3A10.1155%2F2007%2F79090/MediaObjects/13661_2006_Article_665_IEq10_HTML.gif is continuous, symmetric on the interval http://static-content.springer.com/image/art%3A10.1155%2F2007%2F79090/MediaObjects/13661_2006_Article_665_IEq11_HTML.gif , and maybe singular at http://static-content.springer.com/image/art%3A10.1155%2F2007%2F79090/MediaObjects/13661_2006_Article_665_IEq12_HTML.gif and http://static-content.springer.com/image/art%3A10.1155%2F2007%2F79090/MediaObjects/13661_2006_Article_665_IEq13_HTML.gif , http://static-content.springer.com/image/art%3A10.1155%2F2007%2F79090/MediaObjects/13661_2006_Article_665_IEq14_HTML.gif is continuous, and http://static-content.springer.com/image/art%3A10.1155%2F2007%2F79090/MediaObjects/13661_2006_Article_665_IEq15_HTML.gif is symmetric on the interval http://static-content.springer.com/image/art%3A10.1155%2F2007%2F79090/MediaObjects/13661_2006_Article_665_IEq16_HTML.gif for all http://static-content.springer.com/image/art%3A10.1155%2F2007%2F79090/MediaObjects/13661_2006_Article_665_IEq17_HTML.gif and satisfies some appropriate growth conditions. By using Krasnoselskii's fixed point theorem in a cone, we get some existence results of symmetric positive solutions.

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      Authors’ Affiliations

      (1)
      Department of Electron and Information, Zhejiang University of Media and Communications

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      Copyright

      © Y. Sun and X. Zhang. 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.