Next Article in Journal
On the Assumption of the Independence of Thermodynamic Properties on the Gravitational Field
Next Article in Special Issue
Pre-Schauder Bases in Topological Vector Spaces
Previous Article in Journal
Series of Semihypergroups of Time-Varying Artificial Neurons and Related Hyperstructures
Previous Article in Special Issue
Hyers-Ulam Stability for Linear Differences with Time Dependent and Periodic Coefficients
Article

Nonlinear Rayleigh Quotients and Nonlinear Spectral Theory

Raffaele Chiappinelli—Dipartimento di Ingegneria dell’Informazione e Scienze Matematiche, Università di Siena, I-53100 Siena, Italy
Symmetry 2019, 11(7), 928; https://doi.org/10.3390/sym11070928
Received: 21 June 2019 / Revised: 10 July 2019 / Accepted: 12 July 2019 / Published: 16 July 2019
(This article belongs to the Special Issue Nonlinear, Convex, Nonsmooth, Functional Analysis in Symmetry)
We give a new and simplified definition of spectrumfor a nonlinear operator F acting in a real Banach space X, and study some of its features in terms of (qualitative and) quantitative properties of F such as the measure of noncompactness, α ( F ) , of F. Then, using as a main tool the Ekeland Variational Principle, we focus our attention on the spectral properties of F when F is a gradient operator in a real Hilbert space, and in particular on the role played by its Rayleigh quotient R ( F ) and by the best lower and upper bounds, m ( F ) and M ( F ) , of R ( F ) . View Full-Text
Keywords: surjective operators; measure of noncompactness; Darbo’s fixed point theorem; gradient operators; Ekeland variational principle surjective operators; measure of noncompactness; Darbo’s fixed point theorem; gradient operators; Ekeland variational principle
MDPI and ACS Style

Chiappinelli, R. Nonlinear Rayleigh Quotients and Nonlinear Spectral Theory. Symmetry 2019, 11, 928. https://doi.org/10.3390/sym11070928

AMA Style

Chiappinelli R. Nonlinear Rayleigh Quotients and Nonlinear Spectral Theory. Symmetry. 2019; 11(7):928. https://doi.org/10.3390/sym11070928

Chicago/Turabian Style

Chiappinelli, Raffaele. 2019. "Nonlinear Rayleigh Quotients and Nonlinear Spectral Theory" Symmetry 11, no. 7: 928. https://doi.org/10.3390/sym11070928

Find Other Styles
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Article Access Map by Country/Region

1
Back to TopTop