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

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  • Pierluigi Benevieri

    (Instituto de Matemática e Estatística, Universidade de São Paulo, Rua do Matão 1010, 05508-09 São Paulo, Brazil
    The first, second and fourth authors are members of the Gruppo Nazionale per l’Analisi Matematica, la Probabilità e le loro Applicazioni (GNAMPA) of the Istituto Nazionale di Alta Matematica (INdAM).)

  • Alessandro Calamai

    (Dipartimento di Ingegneria Civile, Edile e Architettura, Università Politecnica delle Marche, Via Brecce Bianche, I-60131 Ancona, Italy
    The first, second and fourth authors are members of the Gruppo Nazionale per l’Analisi Matematica, la Probabilità e le loro Applicazioni (GNAMPA) of the Istituto Nazionale di Alta Matematica (INdAM).)

  • 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
    The first, second and fourth authors are members of the Gruppo Nazionale per l’Analisi Matematica, la Probabilità e le loro Applicazioni (GNAMPA) of the Istituto Nazionale di Alta Matematica (INdAM).)

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.

Suggested Citation

  • Pierluigi Benevieri & Alessandro Calamai & Massimo Furi & Maria Patrizia Pera, 2021. "Global Persistence of the Unit Eigenvectors of Perturbed Eigenvalue Problems in Hilbert Spaces: The Odd Multiplicity Case," Mathematics, MDPI, vol. 9(5), pages 1-18, March.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:5:p:561-:d:511714
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