Constant Sign and Nodal Solutions for Problems with the p-Laplacian and a Nonsmooth Potential Using Variational Techniques. (3rd March 2009)

• Record Type: Journal Article
• Authors: Agarwal, Ravi P.; Filippakis, Michael E.; O'Regan, Donal; Papageorgiou, Nikolaos S.
• Other Names: Nieto Juan J. Academic Editor.
• Is Part Of: Boundary value problems. Volume 2009(2009)
• Publication Date: 2009-03-03
• Subjects: Boundary value problems -- Periodicals; Boundary value problems; Electronic journals; Periodicals; 515.35
• DOI: 10.1155/2009/820237
• Languages: English
• ISSNs: 1687-2762

Abstract

Abstract : We consider a nonlinear elliptic equation driven by thep -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 asymptoticallyp -linear problems.