Geodesic
Multiplicity of solutions for gradient systems
Electronic Journal of Differential Equations, Tome 2010 (2010).

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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.
Classification : 35J20, 35J50
Keywords: critical groups, resonance, indefinite weights, Morse theory 
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     author = {da Silva, Edcarlos D.},
     title = {Multiplicity of solutions for gradient systems},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2010},
     year = {2010},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2010__2010__a100/}
}
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da Silva, Edcarlos D. Multiplicity of solutions for gradient systems. Electronic Journal of Differential Equations, Tome 2010 (2010). http://geodesic.mathdoc.fr/item/EJDE_2010__2010__a100/