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Functional Dynamic Equations on Time Scales

  • Book
  • © 2019

Overview

Authors:
  1. Svetlin G. Georgiev

    1. Faculty of Mathematics & Informatics, Sofia University St. Kliment Ohridski, Sorbonne University, Paris, France, Sofia, Bulgaria

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  • This books offers the reader an overview of recent developments of functional dynamic equations on time scales, taking readers beyond the traditional calculus texts.

  • The book introduces functional dynamic equations in relation to mathematical physics applications and problems. Useful tools are provided for investigation for oscillations and nonoscillations of the solutions of functional dynamic equations on time scales.

  • This book is suitable for graduate courses and researchers looking for an introduction to functional dynamic equations on time scales.

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Table of contents (15 chapters)

  1. Front Matter

    Pages i-x
    Download chapter PDF

  2. Calculus on Time Scales

    • Svetlin G. Georgiev
    Pages 1-36

  3. Dynamic Systems

    • Svetlin G. Georgiev
    Pages 37-98

  4. Functional Dynamic Equations. Basic Concepts, Existence, and Uniqueness Theorems

    • Svetlin G. Georgiev
    Pages 99-139

  5. Linear Functional Dynamic Equations

    • Svetlin G. Georgiev
    Pages 141-159

  6. Stability for First-Order Functional Dynamic Equations

    • Svetlin G. Georgiev
    Pages 161-254

  7. Oscillations of First-Order Functional Dynamic Equations

    • Svetlin G. Georgiev
    Pages 255-345

  8. Oscillations of Second-Order Linear Functional Dynamic Equations with a Single Delay

    • Svetlin G. Georgiev
    Pages 347-374

  9. Nonoscillations of Second-Order Functional Dynamic Equations with Several Delays

    • Svetlin G. Georgiev
    Pages 375-406

  10. Oscillations of Second-Order Nonlinear Functional Dynamic Equations

    • Svetlin G. Georgiev
    Pages 407-468

  11. Oscillations of Third-Order Functional Dynamic Equations

    • Svetlin G. Georgiev
    Pages 469-547

  12. Oscillations of Fourth-Order Functional Dynamic Equations

    • Svetlin G. Georgiev
    Pages 549-664

  13. Oscillations of Higher-Order Functional Dynamic Equations

    • Svetlin G. Georgiev
    Pages 665-748

  14. Shift Operators

    • Svetlin G. Georgiev
    Pages 749-780

  15. Impulsive Functional Dynamic Equations

    • Svetlin G. Georgiev
    Pages 781-817

  16. Linear Impulsive Dynamic Systems

    • Svetlin G. Georgiev
    Pages 819-835

  17. Back Matter

    Pages 837-885
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Keywords

About this book

This book is devoted to the qualitative theory of functional dynamic equations on time scales, providing an overview of recent developments in the field as well as a foundation to time scales, dynamic systems, and functional dynamic equations. It discusses functional dynamic equations in relation to mathematical physics applications and problems, providing useful tools for investigation for oscillations and nonoscillations of the solutions of functional dynamic equations on time scales. Practice problems are presented throughout the book for use as a graduate-level textbook and as a reference book for specialists of several disciplines, such as mathematics, physics, engineering, and biology.

Reviews

“This is a complete and interesting book concerning functional dynamic equations on time scales. This book has 15 chapters and 5 appendixes, there are almost 900 pages with a precious content of the theory of time scales ... . This book will be very useful for all mathematicians that work with theory of time scales ... . Also, it can be used as a reference in courses of graduate level.” (Jaqueline Godoy Mesquita, zbMATH 1510.34001, 2023)

Authors and Affiliations

  • Faculty of Mathematics & Informatics, Sofia University St. Kliment Ohridski, Sorbonne University, Paris, France, Sofia, Bulgaria

    Svetlin G. Georgiev

About the author

Svetlin Georgiev is in the Department of Differential Equations of the Faculty of Mathematics and Informatics at Sofia University, Bulgaria.

Bibliographic Information

  • Book Title: Functional Dynamic Equations on Time Scales

  • Authors: Svetlin G. Georgiev

  • DOI: https://doi.org/10.1007/978-3-030-15420-2

  • Publisher: Springer Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer Nature Switzerland AG 2019

  • Hardcover ISBN: 978-3-030-15419-6Published: 14 May 2019

  • eBook ISBN: 978-3-030-15420-2Published: 03 May 2019

  • Edition Number: 1

  • Number of Pages: X, 885

  • Number of Illustrations: 14 illustrations in colour

  • Topics: Functional Analysis

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