Differential and Integral Inequalities

  • Wolfgang Walter

Part of the Ergebnisse der Mathematik und ihrer Grenzgebiete book series (MATHE2, volume 55)

Table of contents

  1. Front Matter
    Pages I-1
  2. Wolfgang Walter
    Pages 2-12
  3. Wolfgang Walter
    Pages 13-62
  4. Wolfgang Walter
    Pages 63-123
  5. Wolfgang Walter
    Pages 179-303
  6. Back Matter
    Pages 304-354

About this book

Introduction

In 1964 the author's mono graph "Differential- und Integral-Un­ gleichungen," with the subtitle "und ihre Anwendung bei Abschätzungs­ und Eindeutigkeitsproblemen" was published. The present volume grew out of the response to the demand for an English translation of this book. In the meantime the literature on differential and integral in­ equalities increased greatly. We have tried to incorporate new results as far as possible. As a matter of fact, the Bibliography has been almost doubled in size. The most substantial additions are in the field of existence theory. In Chapter I we have included the basic theorems on Volterra integral equations in Banach space (covering the case of ordinary differential equations in Banach space). Corresponding theorems on differential inequalities have been added in Chapter II. This was done with a view to the new sections; dealing with the line method, in the chapter on parabolic differential equations. Section 35 contains an exposition of this method in connection with estimation and convergence. An existence theory for the general nonlinear parabolic equation in one space variable based on the line method is given in Section 36. This theory is considered by the author as one of the most significant recent applications of in­ equality methods. We should mention that an exposition of Krzyzanski's method for solving the Cauchy problem has also been added. The numerous requests that the new edition include a chapter on elliptic differential equations have been satisfied to some extent.

Keywords

Banach Space Differentialungleichung Inequalities Integral Integralungleichung differential equation

Authors and affiliations

  • Wolfgang Walter
    • 1
  1. 1.Mathematisches InstitutUniversität KarlsruheKarlsruheGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-86405-6
  • Copyright Information Springer-Verlag Berlin Heidelberg 1970
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-86407-0
  • Online ISBN 978-3-642-86405-6
  • Series Print ISSN 0071-1136
  • About this book