IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-3-030-42117-5_3.html
   My bibliography  Save this book chapter

Functional Dynamical Systems

In: Stability, Periodicity and Boundedness in Functional Dynamical Systems on Time Scales

Author

Listed:
  • Murat Adıvar

    (Fayetteville State University, Broadwell College of Business and Economics)

  • Youssef N. Raffoul

    (University of Dayton, Department of Mathematics)

Abstract

Summary In this chapter we consider functional dynamical systems on time scales that we apply to Volterra integro-dynamic equations on time scales. Volterra integro-dynamic Our general theorems will require the construction of suitable Lyapunov functionals, a task that is difficult but possible. General theorems concerning boundedness and stability of functional dynamical systems on time scales are almost nonexistent and this section is aimed at rectifying the situation. The theorems enable us to qualitatively analyze the theory of boundedness, uniform ultimate boundedness, and stability of solutions of vectors and scalar Volterra integro-dynamic equations. We end the chapter with open problems. Some of the results are new and the rest can be found in Adıvar and Raffoul (Rend Semin Mat Univ Politec Torino 68(4):369–396, 2010), Akın-Bohner and Raffoul (Adv Differ Equ 2006:79689, 18, 2006), and Raffoul (Canad Math Bull 58(1):174–181, 2015; Arch Math 52(1):21–33, 2016).

Suggested Citation

  • Murat Adıvar & Youssef N. Raffoul, 2020. "Functional Dynamical Systems," Springer Books, in: Stability, Periodicity and Boundedness in Functional Dynamical Systems on Time Scales, chapter 0, pages 91-124, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-42117-5_3
    DOI: 10.1007/978-3-030-42117-5_3
    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

    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:978-3-030-42117-5_3. 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.