Abstract and Applied Analysis
Volume 2010 (2010), Article ID 125464, 20 pages
doi:10.1155/2010/125464
Research Article

On the Fredholm Alternative for the Fučík Spectrum

Pavel Drábek1 and Stephen B. Robinson2

1Department of Mathematics and Center N.T.I.S., University of West Bohemia, P.O. Box 314, 306 14 Pilsen, Czech Republic
2Department of Mathematics, Wake Forest University, P.O. Box 7388, Winston-Salem, NC 27109, USA

Received 12 October 2010; Accepted 15 December 2010

Academic Editor: Thomas Bartsch

Copyright © 2010 Pavel Drábek and Stephen B. Robinson. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We consider resonance problems for the one-dimensional 𝑝 -Laplacian assuming Dirichlet boundary conditions. In particular, we consider resonance problems associated with the first three curves of the Fučík Spectrum. Using variational arguments based on linking theorems, we prove sufficient conditions for the existence of at least one solution. Our results are related to the classical Fredholm Alternative for linear operators. We also provide a new variational characterization for points on the third Fučík curve.