Constantin Corduneanu - Functional Differential Equations: Advances and Applications

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CONSTANTIN CORDUNEANU

YIZENG LI

MEHRAN MAHDAVI

Copyright 2016 by John Wiley & Sons, Inc. All rights reserved

Published by John Wiley & Sons, Inc., Hoboken, New Jersey
Published simultaneously in Canada

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Library of Congress Cataloging-in-Publication Data:

Names: Corduneanu, C., author. | Li, Yizeng, 1949 author. | Mahdavi, Mehran, 1959 author.
Title: Functional differential equations : advances and applications/Constantin Corduneanu, Yizeng Li, Mehran Mahdavi.
Description: Hoboken, New Jersey : John Wiley & Sons, Inc., [2016] | Series: Pure and applied mathematics | Includes bibliographical references and index.
Identifiers: LCCN 2015040683 | ISBN 9781119189473 (cloth)
Subjects: LCSH: Functional differential equations.
Classification: LCC QA372 .C667 2016 | DDC 515/.35dc23 LC record available at http://lccn.loc.gov/2015040683

This book is dedicated to the memory of three pioneers of the Theory of Functional Differential Equations:

A.D. MYSHKIS, the author of the first book on non-classical differential equations

N.N. KRASOVSKII, for substantial contributions, particularly for extending Liapunovs method in Stability Theory, to the case of delay equations with finite delay, thus opening the way to the methods of Functional Analysis

J.K. HALE, for creating a vast theory in the study of functional differential equations, by using the modern tools of Functional Analysis

Each created a research school, with many distinguished contributors

The origin of this book is in the research seminar organized by the first coauthor (alphabetically), during the period September 1990 to May 1994, in the Department of Mathematics at The University of Texas at Arlington. The second and the third co-authors were, at that time, Ph.D. students working under the guidance of the first co-author. The seminar was also attended by another Ph.D. student, Zephyrinus Okonkwo, who had been interested in stochastic problems, and sporadically by other members of the Department of Mathematics (among them, Dr. Richard Newcomb II). Visitors also occasionally attended and presented their research results. We mention V. Barbu, Y. Hamaya, M. Kwapisz, I. Gyori, and Cz. Olech. Cooperation between the co-authors continued after the graduation of the co-authors Li and Mahdavi, who attained their academic positions at schools in Texas and Maryland, respectively. All three co-authors continued to pursue the topics that were presented at the seminar and that are included in this book through their Ph.D. theses as well as a number of published papers (single author or jointly). The list of references in this book contains almost all of the contributions that were made during the past two decades (19942014). Separation among the coauthors certainly contributed to the extended period that was needed to carry out the required work.

The book is a monograph, presenting only part of the results available in the literature, mainly mathematical ones, without any claim related to the coverage of the whole field of functional differential equations (FDEs). Paraphrasing the ancient dictum mundum regunt numeri, one can instead say, mundum regunt aequationes. That is why, likely, one finds a large number of reviews dedicated to this field of research, in all the publications concerned with the review of current literature (Mathematical Reviews, Zentralblatt fur Mathematik, Referativnyi Zhurnal, a. o.).

Over 550 items are listed in the Bibliography, all of which have been selected from a much larger number of publications available to the coauthors (i.e., university libraries, preprints, or reprints obtained from authors, papers received for review in view of insertion into various journals, or on the Internet).

The principles of selection were the connections with the topics considered in the book, but also the inclusion of information for themes similar to those treated by the co-authors, but not covered in the book because of the limitations imposed by multiple factors occurring during the preparation of the final text.

Mehran Mahdavi was in charge of the technical realization of the manuscript, a task he carried out with patience and skill. The other co-authors thank him for voluntarily assuming this demanding task, which he accomplished with devotion and competence.

Some developing fields of research related to the study of FDEs, but not included in this books presentations, are the stochastic equations, the fuzzy equations, and the fractional-order functional equations. Some sporadic references are made to discrete argument functional equations, also known as difference equations. While their presence is spotted in many publications, Springer recently dedicated an entire journal to the subject, Advances in Difference Equations (R. P. Agarwal, editor). In addition, Clarendon Press is publishing papers on functional differential equations of the