The Ekeland Variational Principle is used to prove the nonemptiness of the spectrum for positively homogeneous gradient mappings in Hilbert space. Under additional information on the measure of noncompactness of the operator, this leads to the existence of a maximal (or minimal) compact eigenvalue for the operator itself.
Chiappinelli, R. (2008). An application of Ekeland’s Variational Principle to the spectrum of nonlinear homogeneous gradient operators. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 340, 511-520.
An application of Ekeland’s Variational Principle to the spectrum of nonlinear homogeneous gradient operators
CHIAPPINELLI, RAFFAELE
2008-01-01
Abstract
The Ekeland Variational Principle is used to prove the nonemptiness of the spectrum for positively homogeneous gradient mappings in Hilbert space. Under additional information on the measure of noncompactness of the operator, this leads to the existence of a maximal (or minimal) compact eigenvalue for the operator itself.
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