The Brouwer degree associated to classical eigenvalue problems and applications to nonlinear spectral theory

2019/12/06 by Pierluigi Benevieri, Alessandro Calamai, Benevieri, Pierluigi +5
Computer Science · Mathematics · #Advanced Differential Equations and Dynamical Systems #Dynamical Systems (math.DS) #FOS: Mathematics #Matrix Theory and Algorithms #Numerical methods for differential equations #Spectral Theory (math.SP) #math.DS #math.SP

paper · pdf · doi:10.48550/arxiv.1912.03182

20 pages

arxiv created 2019/12/06 · openalex publication_date 2019/12/06 · arxiv updated 2019/12/09 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28

Abstract

Thanks to a connection between two completely different topics, the classical eigenvalue problem in a finite dimensional real vector space and the Brouwer degree for maps between oriented differentiable real manifolds, we were able to solve, at least in the finite dimensional context, a conjecture regarding global continuation in nonlinear spectral theory that we formulated in some recent papers. The infinite dimensional case seems nontrivial, and is still unsolved.

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