Abstract and Applied Analysis
Volume 2010 (2010), Article ID 237826, 22 pages
doi:10.1155/2010/237826
Research Article

Multiplicity of Solutions for Gradient Systems Using Landesman-Lazer Conditions

Edcarlos D. da Silva1,2

1IMECC-UNICAMP, Caixa Postal 6065, CEP 13081-970 Campinas, SP, Brazil
2UFG-IME, Caixa Postal 131, CEP 74001-970 Goiânia, GO, Brazil

Received 22 February 2010; Revised 8 April 2010; Accepted 29 June 2010

Academic Editor: K. Chang

Copyright © 2010 Edcarlos D. da Silva. 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 establish existence and multiplicity of solutions for an elliptic system which presents resonance at infinity of Landesman-Lazer type. In order to describe the resonance, we use an eigenvalue problem with indefinite weights. In all results, we use Variational Methods, Morse Theory and Critical Groups.