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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

Raffaele Chiappinelli 1,

1. 

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

Received  July 2006 Revised  April 2007 Published  September 2007

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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