Eigenvalues of homogeneous gradient mappings in Hilbert space and the Birkoff-Kellogg theorem

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2007, 2007(Special): 260-268. doi: 10.3934/proc.2007.2007.260

Eigenvalues of homogeneous gradient mappings in Hilbert space and the Birkoff-Kellogg theorem

1.	Dipartimento di Scienze Matematiche ed Informatiche, Pian dei Mantellini 44, 53100 Siena, Italy

Received July 2006 Revised April 2007 Published September 2007

Abstract
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It is well known that any (nontrivial) linear compact self-adjoint operator acting in a Hilbert space possesses at least one non-zero eigenvalue. We present a generalization of this to nonlinear mappings as in the title, and discuss the relations of our results with the Birkhoff-Kellogg Theorem on one side, and with the spectral properties of self-adjoint operators on the other.

Keywords: self-adjoint operators, Palais-Smale condition..

Mathematics Subject Classification: Primary: 47J10; Secondary: 47J1.

Citation: Raffaele Chiappinelli. Eigenvalues of homogeneous gradient mappings in Hilbert space and the Birkoff-Kellogg theorem. Conference Publications, 2007, 2007 (Special) : 260-268. doi: 10.3934/proc.2007.2007.260

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