075 An Introduction to Difference Equations.pdf

Undergraduate Texts in Mathematics

Editors

S. Axler

F.W. Gehring

K.A. Ribet

Saber Elaydi

An Introduction to

Difference Equations

Third Edition

Saber Elaydi

Department of Mathematics

Trinity University

San Antonio, Texas 78212

USA

Editorial Board

S. Axler F.W. Gehring K.A. Ribet

Mathematics Department Mathematics Department Department of

San Francisco State

East Hall

Mathematics

University

University of Michigan

University of California

San Francisco, CA 94132

Ann Arbor, MI 48109

at Berkeley

USA

Berkeley, CA 94720-3840

USA

Mathematics Subject Classification (2000): 12031

Library of Congress Cataloging-in-Publication Data

Elaydi, Saber, 1943–

An introduction to difference equations / Saver Elaydi.—3rd ed.

p. cm. — (Undergraduate texts in mathematics)

Includes bibliographical references and index.

ISBN 0-387-23059-9 (acid-free paper)

1. Difference equations.

I. Title.

II. Series.

QA431.E43 2005

515′.625—dc22

2004058916

ISBN 0-387-23059-9

Printed on acid-free paper.

without the written permission of the publisher (Springer Science+Business Media,

Inc., 233 Spring Street, New York, NY 10013, USA), except for brief excerpts in connec-

tion with reviews or scholarly analysis. Use in connection with any form of informa-

tion storage and retrieval, electronic adaptation, computer software, or by similar or

dissimilar methodology now known or hereafter developed is forbidden.

The use in this publication of trade names, trademarks, service marks, and similar

terms, even if they are not identified as such, is not to be taken as an expression of

opinion as to whether or not they are subject to proprietary rights.

Printed in the United States of America.

(MV)

987654321

SPIN 10950678

springeronline.com

Preface to the Third Edition

In contemplating the third edition, I have had multiple objectives to

achieve. The ﬁrst and foremost important objective is to maintain the ac-

cessibility and readability of the book to a broad readership with varying

mathematical backgrounds and sophistication. More proofs, more graphs,

more explanations, and more applications are provided in this edition.

The second objective is to update the contents of the book so that the

reader stays abreast of new developments in this vital area of mathematics.

Recent results on local and global stability of one-dimensional maps are

included in Chapters 1, 4, and Appendices A and C. An extension of the

Hartman–Grobman Theorem to noninvertible maps is stated in Appendix

D. A whole new section on various notions of the asymptoticity of solutions

and a recent extension of Perron’s Second Theorem are added to Chapter

8. In Appendix E a detailed proof of the Levin–May Theorem is presented.

In Chapters 4 and 5, the reader will ﬁnd the latest results on the larval–

pupal–adult ﬂour beetle model.

The third and ﬁnal objective is to better serve the broad readership of

this book by including most, but certainly not all, of the research areas

in diﬀerence equations. As more work is being published in the Journal of

Diﬀerence Equations and Applications and elsewhere, it became apparent

that a whole chapter needed to be dedicated to this enterprise. With the

prodding and encouragement of Gerry Ladas, the new Chapter 5 was born.

Major revisions of this chapter were made by Fozi Dannan, who diligently

and painstakingly rewrote part of the material and caught several errors

and typos. His impact on this edition, particularly in Chapters 1, 4, and

Chapter 8 is immeasurable and I am greatly indebted to him. My thanks

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