Multiplicity of Nontrivial Solutions for Kirchhoff Type Problems

  • Bitao Cheng1,

    Affiliated with

    • Xian Wu2Email author and

      Affiliated with

      • Jun Liu1

        Affiliated with

        Boundary Value Problems20102010:268946

        DOI: 10.1155/2010/268946

        Received: 25 October 2010

        Accepted: 14 December 2010

        Published: 22 December 2010

        Abstract

        By using variational methods, we study the multiplicity of solutions for Kirchhoff type problems http://static-content.springer.com/image/art%3A10.1155%2F2010%2F268946/MediaObjects/13661_2010_Article_910_IEq1_HTML.gif , in http://static-content.springer.com/image/art%3A10.1155%2F2010%2F268946/MediaObjects/13661_2010_Article_910_IEq2_HTML.gif ; http://static-content.springer.com/image/art%3A10.1155%2F2010%2F268946/MediaObjects/13661_2010_Article_910_IEq3_HTML.gif , on http://static-content.springer.com/image/art%3A10.1155%2F2010%2F268946/MediaObjects/13661_2010_Article_910_IEq4_HTML.gif . Existence results of two nontrivial solutions and infinite many solutions are obtained.

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        Authors’ Affiliations

        (1)
        College of Mathematics and Information Science, Qujing Normal University
        (2)
        Department of Mathematics, Yunnan Normal University

        Copyright

        © Bitao Cheng et al. 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.