An application of Ekeland's Variational Principle to the spectrum of nonlinear homogeneous gradient operators |
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| Authors: | Raffaele Chiappinelli |
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| Affiliation: | Dipartimento di Scienze Matematiche ed Informatiche, Pian dei Mantellini 44, I-53100 Siena, Italy |
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| 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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| Keywords: | Compact eigenvalue Normalized eigenset Palais-Smale condition Self-adjoint operator Essential spectrum Singular sequence |
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