Constant Sign and Nodal Solutions for Problems with the -Laplacian and a Nonsmooth Potential Using Variational Techniques
Boundary Value Problems volume 2009, Article number: 820237 (2009)
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.
To access the full article, please see PDF.
About this article
Cite this article
Agarwal, R.P., Filippakis, M.E., O'Regan, D. et al. Constant Sign and Nodal Solutions for Problems with the -Laplacian and a Nonsmooth Potential Using Variational Techniques. Bound Value Probl 2009, 820237 (2009). https://doi.org/10.1155/2009/820237
- Differential Equation
- Partial Differential Equation
- Ordinary Differential Equation
- Functional Equation
- Full Article