Multiplicity of solutions for gradient systems

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...

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Bibliographic Details
Published in:Electronic journal of differential equations 2010-05, Vol.2010 (64), p.1-15
Main Author: Edcarlos D. Da Silva
Format: Article
Language:English
Subjects:
Critical groups
indefinite weights
Morse theory
resonance
Online Access:Get full text
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Summary: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.
ISSN:1072-6691