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Nonlinear Functional Analysis and its Applications

III: Variational Methods and Optimization

  • Eberhard Zeidler

Table of contents

  1. Front Matter
    Pages i-xxii
  2. Introduction to the Subject

    1. Eberhard Zeidler
      Pages 1-11
  3. Introductory Typical Examples

    1. Eberhard Zeidler
      Pages 12-142
  4. Two Fundamental Existence and Uniqueness Principles

    1. Front Matter
      Pages 143-143
    2. Eberhard Zeidler
      Pages 145-167
    3. Eberhard Zeidler
      Pages 168-186
  5. Extremal Problems without Side Conditions

    1. Front Matter
      Pages 187-187
    2. Eberhard Zeidler
      Pages 229-243
  6. Extremal Problems with Smooth Side Conditions

    1. Front Matter
      Pages 271-272
    2. Eberhard Zeidler
      Pages 273-312
    3. Eberhard Zeidler
      Pages 351-360
  7. Extremal Problems with General Side Conditions

    1. Front Matter
      Pages 361-361
    2. Eberhard Zeidler
      Pages 363-378
  8. Saddle Points and Duality

  9. Variational Inequalities

  10. Back Matter
    Pages 599-662

About this book

Introduction

As long as a branch of knowledge offers an abundance of problems, it is full of vitality. David Hilbert Over the last 15 years I have given lectures on a variety of problems in nonlinear functional analysis and its applications. In doing this, I have recommended to my students a number of excellent monographs devoted to specialized topics, but there was no complete survey-type exposition of nonlinear functional analysis making available a quick survey to the wide range of readers including mathematicians, natural scientists, and engineers who have only an elementary knowledge of linear functional analysis. I have tried to close this gap with my five-part lecture notes, the first three parts of which have been published in the Teubner-Texte series by Teubner-Verlag, Leipzig, 1976, 1977, and 1978. The present English edition was translated from a completely rewritten manuscript which is significantly longer than the original version in the Teubner-Texte series. The material is organized in the following way: Part I: Fixed Point Theorems. Part II: Monotone Operators. Part III: Variational Methods and Optimization. Parts IV jV: Applications to Mathematical Physics. The exposition is guided by the following considerations: (a) What are the supporting basic ideas and what intrinsic interrelations exist between them? (/3) In what relation do the basic ideas stand to the known propositions of classical analysis and linear functional analysis? ( y) What typical applications are there? Vll Preface viii Special emphasis is placed on motivation.

Keywords

Mathematica calculus functional analysis optimization

Authors and affiliations

  • Eberhard Zeidler
    • 1
  1. 1.Sektion MathematikLeipzigGerman Democratic Republic

Bibliographic information