A pathological example in nonlinear spectral theory

Advances in Nonlinear Analysis

article

Lorenzo Brasco¹  Giovanni Franzina³ 

[1] Dipartimento di Matematica e Informatica, Università degli Studi di Ferrara;Aix Marseille University, Centrale Marseille;Mathematics Area, Scuola Internazionale Superiore di Studi Avanzati

关键词: Nonlinear eigenvalue problems;    Lusternik–Schnirelmann theory;   

DOI  :  10.1515/anona-2017-0043

学科分类：社会科学、人文和艺术（综合）

来源: De Gruyter

【 摘 要 】

We construct an open set Ω ⊂ ℝ N {\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.

【 授权许可】

CC BY