Japan-United States Seminar on Ordinary Differential and Functional Equations

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243 Japan-United States Seminar on Ordinary Differential and Functional Equations Held in Kyoto/Japan, September 6-11,1971

Edited by Minoru Urabe, Kyoto University, Kyoto/Japan

Springer-Verlag Berlin · Heidelberg· NewYork 1971

AMS Subject Classifications (1970): 28A65, 34Axx, 34Bxx, 34Cxx, 34Dxx, 34Exx, 34F05, 34)xx, 34Kxx, 39Axx, 45)05, 45Mxx, 54H20, 9OD25

ISBN 3-540-05708-0 Springer-Verlag Berlin' Heidelberg· New York ISBN 0-387-05708-0 Springer-Verlag New York· Heidelberg' Berlin This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically those of translation, reprinting, re-use of illustrations, broadcasting, reproduction by photocopying machine or similar means, and storage in data banks. Under § 54 of the German Copyright Law where copies are made for other than private use, a fee is payable to the publisher, the amount of the fee to be determined by agreement with the publisher.

e

by Springer-Verlag Berlin' Heidelberg 1971. Library of Congress Catalog Card Number78-185188.Printed in Germany.

Offsetdruck: Julius Beltz, Hemsbach

PREFACE

A Japan-United States Seminar on Ordinary Differential and Functional Equations was held on September 6 through 11, 1971 at Kyoto International Conference Hall, Kyoto, Japan.

This SEMINAR

as part of the Japan-United States Cooperative Science Program was held under the auspices of the Japan Society for the Promotion of Science and the United States National Science Foundation.

The

coordinators were John A. Nohel, University of Wisconsin, and Minoru Urabe, Research Institute for Mathematical Sciences, Kyoto University. This SEMINAR succeeded the Seminar which has been held on June 26 through 30, 1967 at the University of Minnesota, entitled "United States-Japan Seminar on Differential and Functional Equations". The purpose of this SEMINAR was to stimulate further the cooperative efforts of research mathematicians in both countries who have contributed to the development of the theories of ordinary differential and functional equations. These Proceedings are composed of two sections.

Section I

contains the texts of all major addresses and Section II contains the reports of short communications. The coordinators of this SEMINAR owe a great debt of gratitude to the supporting organizations, the Japan Society for the Promotion of Science and the United States National Science Foundation. Special thanks are due to the SEMINAR participants whose unhesitating and generous contribution of their time and work made possible the SEMINAR and these Proceedings.

CONTENTS

SECTION I Difference inequalities and their applications to stability problem S. SUGIYAMA

1

Selected topics in differential delay equations J. A. YORKE

16

Stability for almost periodic systems T. YOSHIZAWA

29

Perturbations of Volterra equations and admissibility •. J. A. NOHEL

40

On Liapunov-Razumikhin type theorems J. KATo

On a nonlinear Volterra equation J. J. LEVIN

66

Local dynamical systems and their isomorphisms

76

T. UR