IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v9y2021i5p561-d511714.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/9/5/561/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/9/5/561/
    Download Restriction: no
    ---><---

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:9:y:2021:i:5:p:561-:d:511714. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.