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Open Access Open Badges Research Article

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

Jing Zhang* and Xiaoping Xue

Author Affiliations

Department of Mathematics, Harbin Institute of Technology, Harbin 150025, China

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Boundary Value Problems 2011, 2011:214289  doi:10.1155/2011/214289

The electronic version of this article is the complete one and can be found online at: http://www.boundaryvalueproblems.com/content/2011/1/214289

Received:29 June 2010
Revisions received:7 November 2010
Accepted:18 January 2011
Published:26 January 2011

© 2011 Jing Zhang and Xiaoping Xue.

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.


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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