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Nonlinear Functional Analysis and its Applications

III: Variational Methods and Optimization

  • Textbook
  • © 1985

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Authors:
  1. Eberhard Zeidler

    1. Sektion Mathematik, Leipzig, German Democratic Republic

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Table of contents (22 chapters)

  1. Front Matter

    Pages i-xxii
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  2. Introduction to the Subject

    1. Introduction to the Subject

      • Eberhard Zeidler
      Pages 1-11

  3. Introductory Typical Examples

    1. Introductory Typical Examples

      • Eberhard Zeidler
      Pages 12-142

  4. Two Fundamental Existence and Uniqueness Principles

    1. Front Matter

      Pages 143-143
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    2. Compactness and Extremal Principles

      • Eberhard Zeidler
      Pages 145-167

    3. Convexity and Extremal Principles

      • Eberhard Zeidler
      Pages 168-186

  5. Extremal Problems without Side Conditions

    1. Front Matter

      Pages 187-187
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    2. Free Local Extrema of Differentiable Functionals and the Calculus of Variations

      • Eberhard Zeidler
      Pages 189-228

    3. Potential Operators

      • Eberhard Zeidler
      Pages 229-243

    4. Free Minima for Convex Functionals, Ritz Method and the Gradient Method

      • Eberhard Zeidler
      Pages 244-269

  6. Extremal Problems with Smooth Side Conditions

    1. Front Matter

      Pages 271-272
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    2. Lagrange Multipliers and Eigenvalue Problems

      • Eberhard Zeidler
      Pages 273-312

    3. Ljusternik-Schnirelman Theory and the Existence of Several Eigenvectors

      • Eberhard Zeidler
      Pages 313-350

    4. Bifurcation for Potential Operators

      • Eberhard Zeidler
      Pages 351-360

  7. Extremal Problems with General Side Conditions

    1. Front Matter

      Pages 361-361
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    2. Differentiable Functionals on Convex Sets

      • Eberhard Zeidler
      Pages 363-378

    3. Convex Functionals on Convex Sets and Convex Analysis

      • Eberhard Zeidler
      Pages 379-406

    4. General Lagrange Multipliers (Dubovickii-Miljutin Theory)

      • Eberhard Zeidler
      Pages 407-452

  8. Saddle Points and Duality

    1. Front Matter

      Pages 453-455
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    2. General Duality Principle by Means of Lagrange Functions and Their Saddle Points

      • Eberhard Zeidler
      Pages 457-478
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Keywords

About this book

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.

Authors and Affiliations

  • Sektion Mathematik, Leipzig, German Democratic Republic

    Eberhard Zeidler

Bibliographic Information

  • Book Title: Nonlinear Functional Analysis and its Applications

  • Book Subtitle: III: Variational Methods and Optimization

  • Authors: Eberhard Zeidler

  • DOI: https://doi.org/10.1007/978-1-4612-5020-3

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media New York 1985

  • Hardcover ISBN: 978-0-387-90915-8

  • Softcover ISBN: 978-1-4612-9529-7

  • eBook ISBN: 978-1-4612-5020-3

  • Edition Number: 1

  • Number of Pages: XXII, 662

  • Additional Information: Original German edition in 3 volumes published by Teubner Verlag, Leipzig, 1975/76/77

  • Topics: Systems Theory, Control, Calculus of Variations and Optimal Control; Optimization, Analysis

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