Skip to content

Advertisement

  • Research Article
  • Open Access

Constant Sign and Nodal Solutions for Problems with the -Laplacian and a Nonsmooth Potential Using Variational Techniques

  • 1Email author,
  • 2,
  • 3 and
  • 4
Boundary Value Problems20092009:820237

https://doi.org/10.1155/2009/820237

  • Received: 10 December 2008
  • Accepted: 23 January 2009
  • Published:

Abstract

We consider a nonlinear elliptic equation driven by the -Laplacian with a nonsmooth potential (hemivariational inequality) and Dirichlet boundary condition. Using a variational approach based on nonsmooth critical point theory together with the method of upper and lower solutions, we prove the existence of at least three nontrivial smooth solutions: one positive, the second negative, and the third sign changing (nodal solution). Our hypotheses on the nonsmooth potential incorporate in our framework of analysis the so-called asymptotically -linear problems.

Keywords

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

Publisher note

To access the full article, please see PDF.

Authors’ Affiliations

(1)
Department of Mathematical Sciences, Florida Institute of Technology, Melbourne, FL 32901-6975, USA
(2)
Department of Mathematics, Hellenic Army Academy, Vari, 16673, Athens, Greece
(3)
Department of Mathematics, National University of Ireland, Galway, Ireland
(4)
Department of Mathematics, National Technical University, Zografou Campus, 15780 Athens, Greece

Copyright

Advertisement