Skip to main content

Advertisement

Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

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

  • 1302 Accesses

  • 5 Citations

Abstract

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.

Publisher note

To access the full article, please see PDF.

Author information

Correspondence to Jing Zhang.

Rights and permissions

Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Reprints and Permissions

About this article

Cite this article

Zhang, J., Xue, X. Multiple Solutions of -Laplacian with Neumann and Robin Boundary Conditions for Both Resonance and Oscillation Problem. Bound Value Probl 2011, 214289 (2011). https://doi.org/10.1155/2011/214289

Download citation

Keywords

  • Differential Equation
  • Partial Differential Equation
  • Ordinary Differential Equation
  • Functional Equation
  • Full Article