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Open Access 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

Published: 26 January 2011

Abstract

We discuss Neumann and Robin problems driven by the -Laplacian with jumping nonlinearities. Using sub-sup solution method, FucĂ­k 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.