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

Pages: 260 - 268, Issue Special, September 2007

 Abstract        Full Text (194.2K)              

Raffaele Chiappinelli - Dipartimento di Scienze Matematiche ed Informatiche, Pian dei Mantellini 44, 53100 Siena, Italy (email)

Abstract: 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: 47J10.

Received: July 2006;      Revised: April 2007;      Published: September 2007.