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.

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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
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description 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.
doi_str_mv 10.1515/anona-2017-0043
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source De Gruyter journals
subjects 35P30
47A75
58E05
Lusternik–Schnirelmann theory
Nonlinear eigenvalue problems
title A pathological example in nonlinear spectral theory
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