Multiple Solutions of -Laplacian with Neumann and Robin Boundary Conditions for Both Resonance and Oscillation Problem

  • Jing Zhang1Email author and

    Affiliated with

    • Xiaoping Xue1

      Affiliated with

      Boundary Value Problems20112011:214289

      DOI: 10.1155/2011/214289

      Received: 29 June 2010

      Accepted: 18 January 2011

      Published: 26 January 2011


      We discuss Neumann and Robin problems driven by the -Laplacian with jumping nonlinearities. Using sub-sup solution method, Fucík spectrum, mountain pass theorem, degree theorem together with suitable truncation techniques, we show that the Neumann problem has infinitely many nonconstant solutions and the Robin problem has at least four nontrivial solutions. Furthermore, we study oscillating equations with Robin boundary and obtain infinitely many nontrivial solutions.

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      Authors’ Affiliations

      Department of Mathematics, Harbin Institute of Technology


      © J. Zhang and X. Xue. 2011

      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.