Global Persistence of the Unit Eigenvectors of Perturbed Eigenvalue Problems in Hilbert Spaces: The Odd Multiplicity Case

Pierluigi Benevieri, Alessandro Calamai, Massimo Furi and Maria Patrizia Pera
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Pierluigi Benevieri: Instituto de Matemática e Estatística, Universidade de São Paulo, Rua do Matão 1010, 05508-09 São Paulo, Brazil
Alessandro Calamai: Dipartimento di Ingegneria Civile, Edile e Architettura, Università Politecnica delle Marche, Via Brecce Bianche, I-60131 Ancona, Italy
Massimo Furi: Dipartimento di Matematica e Informatica “Ulisse Dini”, Università degli Studi di Firenze, Via S. Marta 3, I-50139 Florence, Italy
Maria Patrizia Pera: Dipartimento di Matematica e Informatica “Ulisse Dini”, Università degli Studi di Firenze, Via S. Marta 3, I-50139 Florence, Italy

Mathematics, 2021, vol. 9, issue 5, 1-18

Abstract: We study the persistence of eigenvalues and eigenvectors of perturbed eigenvalue problems in Hilbert spaces. We assume that the unperturbed problem has a nontrivial kernel of odd dimension and we prove a Rabinowitz-type global continuation result. The approach is topological, based on a notion of degree for oriented Fredholm maps of index zero between real differentiable Banach manifolds.

Keywords: eigenvalues; eigenvectors; nonlinear spectral theory; topological degree; bifurcation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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