Electron. J. Diff. Equ., Vol. 2010(2010), No. 64, pp. 1-15.

Multiplicity of solutions for gradient systems

Edcarlos D. da Silva

We establish the existence of nontrivial solutions for an elliptic system which is resonant both at the origin and at infinity. The resonance is given by an eigenvalue problem with indefinite weight, and the nonlinear term is permitted to be unbounded. Also, we consider the case where the resonance at infinity and at the origin can occur with different weights. Our main tool is the computation of critical groups.

Submitted January 25, 2010. Published May 5, 2010.
Math Subject Classifications: 35J20, 35J50.
Key Words: Critical groups; resonance; indefinite weights; Morse theory

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Edcarlos D. da Silva
IMECC-UNICAMP, CP 6065, 13081-970, Campinas-SP, Brazil.
IME-UFG -Instituto de Matemática e Estatística
CP 131 CEP 74001-970 - Goiâ:nia - Goiás, Brazil
email: eddomingos@mat.ufg.br, eddomingos@hotmail.com

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