Electronic Journal of Differential Equations,
Vol. 2010(2010), No. 64, pp. 1-15.

Title: Multiplicity of solutions for gradient systems

Author: Edcarlos D. da Silva (IMECC-UNICAMP, Campinas-SP, Brazil)
	 
Abstract:
 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 05, 2010.
Math Subject Classifications: 35J20, 35J50.
Key Words: Critical groups; resonance; indefinite weights; Morse theory