IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-1-4614-3455-9_13.html
   My bibliography  Save this book chapter

Second-Order Linear Delay Impulsive Differential Equations

In: Nonoscillation Theory of Functional Differential Equations with Applications

Author

Listed:
  • Ravi P. Agarwal

    (Texas A&M University—Kingsville, Department of Mathematics)

  • Leonid Berezansky

    (Ben-Gurion University of the Negev, Department of Mathematics)

  • Elena Braverman

    (University of Calgary, Department of Mathematics)

  • Alexander Domoshnitsky

    (Ariel University Center of Samaria, Department of Computer Sciences and Mathematics)

Abstract

In Chap. 13, second-order linear delay impulsive differential equations are considered. First, the equivalence of the four properties for a second-order impulsive delay equations is established: nonoscillation of the differential equation and of the corresponding differential inequality, positivity of the fundamental function and the existence of a solution of the generalized Riccati inequality. Further, comparison theorems, as well as explicit oscillation and nonoscillation conditions are justified. In the particular case when the values of impulses for the solution and its derivative match, a special nonimpulsive delay differential equation is constructed such that oscillation of an impulsive equation is equivalent to oscillation of the constructed nonimpulsive equation. As a consequence of this theorem, sharper nonoscillation results for this case of impulsive conditions are obtained, and oscillation properties of a second-order impulsive equation and some specially constructed nonimpulsive equation can be compared.

Suggested Citation

  • Ravi P. Agarwal & Leonid Berezansky & Elena Braverman & Alexander Domoshnitsky, 2012. "Second-Order Linear Delay Impulsive Differential Equations," Springer Books, in: Nonoscillation Theory of Functional Differential Equations with Applications, edition 127, chapter 0, pages 301-318, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4614-3455-9_13
    DOI: 10.1007/978-1-4614-3455-9_13
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a
    for a similarly titled item that would be available.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    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:spr:sprchp:978-1-4614-3455-9_13. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.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.