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Stability Theory and the Existence of Periodic Solutions and Almost Periodic Solutions

  • T. Yoshizawa

Part of the Applied Mathematical Sciences book series (AMS, volume 14)

Table of contents

  1. Front Matter
    Pages i-vii
  2. T. Yoshizawa
    Pages 1-39
  3. T. Yoshizawa
    Pages 40-162
  4. Back Matter
    Pages 224-233

About this book

Introduction

Since there are several excellent books on stability theory, the author selected some recent topics in stability theory which are related to existence theorems for periodic solutions and for almost periodic solutions. The author hopes that these notes will also serve as an introduction to stability theory. These notes contain stability theory by Liapunov's second method and somewhat extended discussion of stability properties in almost periodic systems, and the existence of a periodic solution in a periodic system is discussed in connection with the boundedness of solutions, and the existence of an almost periodic solution in an almost periodic system is considered in con­ nection with some stability property of a bounded solution. In the theory of almost periodic systems, one has to consider almost periodic functions depending on parameters, but most of text books on almost periodic functions do not contain this case. Therefore, as mathemati­ cal preliminaries, the first chapter is intended to provide a guide for some properties of almost periodic functions with parameters as well as for properties of asymptotically almost periodic functions. These notes originate from a seminar on stability theory given by the author at the Mathematics Department of Michigan State Univer­ sity during the academic year 1972-1973. The author is very grateful to Professor Pui-Kei Wong and members of the Department for their warm hospitality and many helpful conversations. The author wishes to thank Mrs.

Keywords

Differentialgleichung Fastperiodische Funktion Stability Stabilität equation function linear optimization mathematics theorem

Authors and affiliations

  • T. Yoshizawa
    • 1
  1. 1.Mathematical InstituteTohoku UniversitySendaiJapan

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4612-6376-0
  • Copyright Information Springer-Verlag New York 1975
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-0-387-90112-1
  • Online ISBN 978-1-4612-6376-0
  • Series Print ISSN 0066-5452
  • Buy this book on publisher's site