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arXiv · 1707.00867

A pathological example in Nonlinear Spectral Theory

Lorenzo Brasco·Giovanni Franzina
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Abstract

We construct an open set $Ω\subset\mathbb{R}^N$ 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.

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Lorenzo Brasco, Giovanni Franzina. 2017-07-04. A pathological example in Nonlinear Spectral Theory. https://arxiv.org/abs/1707.00867

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