A pathological example in nonlinear spectral theory

We construct an open set on which an eigenvalue problem for the -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.

Saved in:
Bibliographic Details
Published in:Advances in nonlinear analysis 2017-08, Vol.8 (1), p.707-714
Main Authors: Brasco, Lorenzo, Franzina, Giovanni
Format: Article
Language:English
Subjects:
35P30
47A75
58E05
Lusternik–Schnirelmann theory
Nonlinear eigenvalue problems
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We construct an open set on which an eigenvalue problem for the -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.
ISSN:2191-9496
2191-950X
DOI:10.1515/anona-2017-0043