Functional Dynamic Equations on Time Scales
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 discusse
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Functional Dynamic Equations on Time Scales
Functional Dynamic Equations on Time Scales
Svetlin G. Georgiev
Functional Dynamic Equations on Time Scales
123
Svetlin G. Georgiev Faculty of Mathematics & Informatics Sofia University St. Kliment Ohridski Sofia, Bulgaria Sorbonne University, Paris, France
ISBN 978-3-030-15419-6 ISBN 978-3-030-15420-2 (eBook) https://doi.org/10.1007/978-3-030-15420-2 Library of Congress Control Number: 2019935571 Mathematics Subject Classification: 39A10, 34A60, 34B37, 34C10, 34K20, 34K30 © Springer Nature Switzerland AG 2019 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, express 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
Preface
This book is devoted to qualitative theory of functional dynamic equations on time scales and summarizes the most recent contributions in this area. The book is intended for senior undergraduate students and beginning graduate students of engineering and science courses. There are fifteen chapters in this book, which in the book are pedagogically organized. Each chapter is concluded by a section with practical problems. In Chapter 1, the basic definitions of forward and backward jump operators are provided, as well as the graininess function. They are introduced the definitions for delta derivative and delta integral and they are given some of their properties. They are deducted some of the basic properties of the power series. Chapter 2 introduces dynamic systems on time scales. They are considered dynamic systems with constant coefficients. They are given some applications of the nonlinear dynamic equations on time scales to certain real life problems. Chapter 3 deals with the classification of functional dynamic equations, the method of steps, there are formulated and proved
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