Variational Methods

Applications to Nonlinear Partial Differential Equations and Hamiltonian Systems

  • Michael Struwe

Table of contents

  1. Front Matter
    Pages I-XIV
  2. Michael Struwe
    Pages 66-153
  3. Michael Struwe
    Pages 154-210
  4. Back Matter
    Pages 211-244

About this book

Introduction

It would be hopeless to attempt to give a complete account of the history of the calculus of variations. The interest of Greek philosophers in isoperimetric problems underscores the importance of "optimal form" in ancient cultures, see Hildebrandt-Tromba [1] for a beautiful treatise of this subject. While variatio­ nal problems thus are part of our classical cultural heritage, the first modern treatment of a variational problem is attributed to Fermat (see Goldstine [1; p.l]). Postulating that light follows a path of least possible time, in 1662 Fer­ mat was able to derive the laws of refraction, thereby using methods which may already be termed analytic. With the development of the Calculus by Newton and Leibniz, the basis was laid for a more systematic development of the calculus of variations. The brothers Johann and Jakob Bernoulli and Johann's student Leonhard Euler, all from the city of Basel in Switzerland, were to become the "founding fathers" (Hildebrandt-Tromba [1; p.21]) of this new discipline. In 1743 Euler [1] sub­ mitted "A method for finding curves enjoying certain maximum or minimum properties", published 1744, the first textbook on the calculus of variations.

Keywords

Hamilton Systeme Hamiltonian Systems Palais-Smale condition Partial Differential Equations Perturbation Störungstheorie Variational Methods Variationsrechnung calculus differential equation maximum minimum partieller Differentialgleichungen

Authors and affiliations

  • Michael Struwe
    • 1
  1. 1.ETH-ZentrumMathematik, ETH ZürichZürichSwitzerland

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-662-02624-3
  • Copyright Information Springer-Verlag Berlin Heidelberg 1990
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-662-02626-7
  • Online ISBN 978-3-662-02624-3
  • About this book