Grasping the phantom – a new approach to nonlinear spectral theory

2001 ◽  
Vol 180 (3) ◽  
pp. 255-284 ◽  
Author(s):  
P. Santucci ◽  
M. Väth
Keyword(s):  
Spectral Theory ◽  
New Approach ◽  
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.

Nonlinear Spectral Theory

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