nonlinear spectral theory
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Author(s):  
Pierluigi Benevieri ◽  
Alessandro Calamai ◽  
Massimo Furi ◽  
Maria Patrizia Pera





Symmetry ◽  
2019 ◽  
Vol 11 (7) ◽  
pp. 928 ◽  
Author(s):  
Raffaele Chiappinelli

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 ) .





2017 ◽  
Vol 8 (1) ◽  
pp. 707-714 ◽  
Author(s):  
Lorenzo Brasco ◽  
Giovanni Franzina

Abstract We construct an open set {\Omega\subset\mathbb{R}^{N}} on which an eigenvalue problem for the p-Laplacian has no isolated first eigenvalue and the spectrum is not discrete. The same example shows that the usual Lusternik–Schnirelmann minimax construction does not exhaust the whole spectrum of this eigenvalue problem.



Author(s):  
Jürgen Appell ◽  
Espedito De Pascale ◽  
Alfonso Vignoli


2002 ◽  
Vol 51 (1) ◽  
pp. 171-188 ◽  
Author(s):  
G. Infante ◽  
J.R.L. Webb






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