A degree associated to linear eigenvalue problems in Hilbert spaces and\n applications to nonlinear spectral theory

2020/06/28 by Pierluigi Benevieri, Alessandro Calamai, Benevieri, Pierluigi +5
Computer Science · Engineering · Mathematics · #34C23 #47A75 #47H11 #47J10 #55M25 #Advanced Differential Equations and Dynamical Systems #FOS: Mathematics #Matrix Theory and Algorithms #Spectral Theory (math.SP) #Stability and Control of Uncertain Systems

paper · pdf · doi:10.48550/arxiv.2006.15539

openalex publication_date 2020/06/28 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28

Abstract

We extend to the infinite dimensional context the link between two completely\ndifferent topics recently highlighted by the authors: the classical eigenvalue\nproblem for real square matrices and the Brouwer degree for maps between\noriented finite dimensional real manifolds. Thanks to this extension, we solve\na conjecture regarding global continuation in nonlinear spectral theory that we\nhave formulated in a recent article. Our result (the ex conjecture) is applied\nto prove a Rabinowitz type global continuation property of the solutions to a\nperturbed motion equation containing an air resistance frictional force.\n

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