Theory of Functional Differential Equations
Since the publication of my lecture notes, Functional Differential Equations in the Applied Mathematical Sciences series, many new developments have occurred. As a consequence, it was decided not to make a few corrections and additions for a second editio
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Theory of Functional Differential Equations
Springer-Verlag New York Heidelberg
Berlin
Jack K. Hale Division of Applied Mathematics Brown University Providence, Rhode Island 02912
Editors Fritz John
Lawrence Sirovich
Courant Institute of Mathematical Studies New York University New York, N.Y. 10012
Division of Applied Mathematics Brown University Providence, R.1. 02912
Joseph P. LaSalle
Gerald B. Whitham
Division of Applied Mathematics Brown University Providence, R.1. 02912
Applied Mathematics Firestone Laboratory California Institute of Technology Pasadena, CA. 91125
AMS Subject Classifications 34Jxx, 34Kxx, 34A30, 34C25, 34C35, 34DIO, 34D20, 35H05
Library of Congress Cataloging in Publication Data Hale, Jack K. 1928Theory of functional differential equations. (Applied mathematical sciences; v. 3) First ed. published in 1971 under title: Functional differential equations. Bibliography: p. 1. Functional differential equations. I. Title. II. Series. 515'.35 76-26611 QAI.A647 vol. 3 1977 [QA372]
All rights reserved. No part of this book may be translated or reproduced in any form without permission from Springer-Verlag.
© 1977 by Springer-Verlag New York Inc.
Softcover reprint of the hardcover 2nd edition 1977
ISBN -13: 978-1-4612-9894-6 e-ISBN-13: 978-1-4612-9892-2 DOT: 10.1007/978-1-4612-9892-2
Applied Mathematical Sciences I Volume 3
Preface
Since the publication of my lecture notes, Functional Differential Equations in the Applied Mathematical Sciences series, many new developments have occurred. As a consequence, it was decided not to make a few corrections and additions for a second edition of those notes, but to present a more comprehensive theory. The present work attempts to consolidate those elements of the theory which have stabilized and also to include recent directions of research. The following chapters were not discussed in my original notes. Chapter 1 is an elementary presentation of linear differential difference equations with constant coefficients of retarded and neutral type. Chapter 4 develops the recent theory of dissipative systems. Chapter 9 is a new chapter on perturbed systems. Chapter 11 is a new presentation incorporating recent results on the existence of periodic solutions of autonomous equations. Chapter 12 is devoted entirely to neutral equations. Chapter 13 gives an introduction to the global and generic theory. There is also an appendix on the location of the zeros of characteristic polynomials. The remainder of the material has been completely revised and updated with the most significant changes occurring in Chapter 3 on the properties of solutions, Chapter 5 on stability, and Chapter lOon behavior near a periodic orbit. It is impossible to thank individually by name all my friends, colleagues, and students who have helped me over the years to understand something about functional differential equations. Each of these persons will recognize their influence on the presentation. However, Chapter 13 on the global theory could not have been written without the
