Global persistence of the unit eigenvectors of perturbed eigenvalue\n problems in Hilbert spaces: the odd multiplicity case

2021/01/08 by Pierluigi Benevieri, Alessandro Calamai, Benevieri, Pierluigi +5
Mathematics · #47A75 #47H11 #47J10 #55M25 #Differential Equations and Numerical Methods #FOS: Mathematics #Nonlinear Differential Equations Analysis #Numerical methods for differential equations #Spectral Theory (math.SP)

paper · pdf · doi:10.48550/arxiv.2101.02910

openalex publication_date 2021/01/08 · openalex created_date 2022/02/25 · openalex updated_date 2026/07/28

Abstract

We study the persistence of eigenvalues and eigenvectors of perturbed\neigenvalue problems in Hilbert spaces. We assume that the unperturbed problem\nhas a nontrivial kernel of odd dimension and we prove a Rabinowitz-type global\ncontinuation result. The approach is topological, based on a notion of degree\nfor oriented Fredholm maps of index zero between real differentiable Banach\nmanifolds.\n

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