Stability, Periodicity and Boundedness in Functional Dynamical Systems on Time Scales
Motivated by recent increased activity of research on time scales, the book provides a systematic approach to the study of the qualitative theory of boundedness, periodicity and stability of Volterra integro-dynamic equations on time scales. Researc
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ability, Periodicity and Boundedness in Functional Dynamical Systems on Time Scales
Stability, Periodicity and Boundedness in Functional Dynamical Systems on Time Scales
Murat Adıvar • Youssef N. Raffoul
Stability, Periodicity and Boundedness in Functional Dynamical Systems on Time Scales
Murat Adıvar Broadwell College of Business and Economics Fayetteville State University Fayetteville, NC, USA
Youssef N. Raffoul Department of Mathematics University of Dayton Dayton, OH, USA
ISBN 978-3-030-42116-8 ISBN 978-3-030-42117-5 (eBook) https://doi.org/10.1007/978-3-030-42117-5 Mathematics Subject Classification (2010): 34NXX, 34N05, 34C25, 34K20, 34K37, 34K38, 34K40, 39A05, 39A06, 39A12, 39A60 © Springer Nature Switzerland AG 2020 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland
Dedicated to the memory of my father Ali Akın Adıvar and my mother Muzaffer Adıvar who have worked tirelessly and relentlessly to provide their children with better lives.
Dedicated to my wife Burcu Adıvar, who has always supported my ambition: you are always and will be my perfect love and perfect role model to our children Buket and Aliakın. — Murat Adıvar
To my strong and beautiful wife Nancy and my wonderful children Hannah, Venicia, Paul, Joseph, and Daniel. — Youssef N. Raffoul
Preface
The book provides an integrated approach to the study of the qualitative theory of dynamical systems on time scales. It is aimed at postgraduate students and researchers with basic knowledge in calculus, differential equations, difference equations real analysis, and familiarity with time scales. The area of time scales is relatively new and advanced topics such as existence of solutions, boundedness, stability, and the existence of per
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