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.
We consider resonance problems for the one-dimensional -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