scholarly journals The Brouwer degree associated to classical eigenvalue problems and applications to nonlinear spectral theory

2021 ◽  
pp. 1-25
Author(s):  
Pierluigi Benevieri ◽  
Alessandro Calamai ◽  
Massimo Furi ◽  
Maria Patrizia Pera
Keyword(s):  
Spectral Theory ◽  
Eigenvalue Problems ◽  
Brouwer Degree ◽  
Nonlinear Spectral Theory

scholarly journals A pathological example in nonlinear spectral theory

2017 ◽  
Vol 8 (1) ◽  
pp. 707-714 ◽  
Author(s):  
Lorenzo Brasco ◽  
Giovanni Franzina
Keyword(s):  
Eigenvalue Problem ◽  
Spectral Theory ◽  
First Eigenvalue ◽  
Open Set ◽  
Lusternik Schnirelmann ◽  
Nonlinear Spectral Theory

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.

Using a nonlinear spectral theory to solve boundary value problems

1981 ◽  
Vol 5 (9) ◽  
pp. 1037-1042 ◽  
Author(s):  
Giuseppe Conti ◽  
Rita Iannacci
Keyword(s):  
Boundary Value Problems ◽  
Spectral Theory ◽  
Boundary Value ◽  
Nonlinear Spectral Theory

Nonlinear Spectral Theory

2004 ◽  
Author(s):  
Jürgen Appell ◽  
Espedito De Pascale ◽  
Alfonso Vignoli
Keyword(s):  
Spectral Theory ◽  
Nonlinear Spectral Theory

A finite dimensional approach to nonlinear spectral theory

2002 ◽  
Vol 51 (1) ◽  
pp. 171-188 ◽  
Author(s):  
G. Infante ◽  
J.R.L. Webb
Keyword(s):  
Spectral Theory ◽  
Dimensional Approach ◽  
Finite Dimensional ◽  
Nonlinear Spectral Theory
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