An application of Ekeland’s Variational Principle to the spectrum of nonlinear homogeneous gradient operators

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. © 2007 Elsevier Inc. All rights reserved