IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v251y2015icp92-107.html
   My bibliography  Save this article

Generalized oscillation theorems for symplectic difference systems with nonlinear dependence on spectral parameter

Author

Listed:
  • Elyseeva, Julia

Abstract

In this paper we generalize oscillation theorems for discrete symplectic eigenvalue problems with nonlinear dependence on spectral parameter recently proved by R. Šimon Hilscher and W. Kratz under the assumption that the block Bk(λ) of the symplectic coefficient matrices located in the right upper corner has a constant image for all λ∈R. In our version of the discrete oscillation theorems we avoid this assumption admitting that rankBk(λ) is a piecewise constant function of the spectral parameter λ. Assuming a monotonicity condition for the symplectic coefficient matrices we show that spectrum of symplectic eigenvalue problems with the Dirichlet boundary conditions is bounded from below iff so is the number of jump discontinuities of rankBk(λ).

Suggested Citation

  • Elyseeva, Julia, 2015. "Generalized oscillation theorems for symplectic difference systems with nonlinear dependence on spectral parameter," Applied Mathematics and Computation, Elsevier, vol. 251(C), pages 92-107.
    • Handle: RePEc:eee:apmaco:v:251:y:2015:i:c:p:92-107
    DOI: 10.1016/j.amc.2014.11.042
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300314015744
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2014.11.042?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Elyseeva, Julia, 2018. "The comparative index and transformations of linear Hamiltonian differential systems," Applied Mathematics and Computation, Elsevier, vol. 330(C), pages 185-200.

    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:eee:apmaco:v:251:y:2015:i:c:p:92-107. 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: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    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.