2001-Luminy conference on Quasilinear Elliptic and Parabolic Equations and Systems
Electron. J. Diff. Eqns., Conf. 08, 2002, pp. 103-120.

### Geometry of the energy functional and the Fredholm alternative for the p-Laplacian in higher dimensions Pavel Drabek

Abstract:
In this paper we study Dirichlet boundary-value problems, for the p-Laplacian, of the form

where is a bounded domain with smooth boundary , , and is the first eigenvalue of . We study the geometry of the energy functional

and show the difference between the case and the case . We also give the characterization of the right hand sides for which the Dirichlet problem above is solvable and has multiple solutions.

Show me the PDF file (258K), TEX file, and other files for this article.

 Pavel Drabek Centre of Applied Mathematics University of West Bohemia P. O. Box 314, 306 14 Plzen, Czech Republic e-mail: pdrabek@kma.zcu.cz