Calculus of Variations and Geometric Measure Theory

L. Brasco - G. Franzina

A pathological example in Nonlinear Spectral Theory

created by brasco on 24 Feb 2017
modified on 04 Jul 2017


Accepted Paper

Inserted: 24 feb 2017
Last Updated: 4 jul 2017

Journal: Adv. Nonlinear Anal.
Pages: 9
Year: 2017

We construct an open set $\Omega\subset\mathbb{R}^N$ on which an eigenvalue problem for the $p-$Laplacian has not 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.

Keywords: p-Laplacian, Nonlinear eigenvalue problems, Lusternik-Schnirelmann theory