Nonlinear Functional Analysis and Its Applications

II/ A: Linear Monotone Operators

  • Eberhard Zeidler

Table of contents

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

  3. Linear Monotone Problems

About this book

Introduction

This is the second of a five-volume exposition of the main principles of nonlinear functional analysis and its applications to the natural sciences, economics, and numerical analysis. The presentation is self -contained and accessible to the nonspecialist. Part II concerns the theory of monotone operators. It is divided into two subvolumes, II/A and II/B, which form a unit. The present Part II/A is devoted to linear monotone operators. It serves as an elementary introduction to the modern functional analytic treatment of variational problems, integral equations, and partial differential equations of elliptic, parabolic and hyperbolic type. This book also represents an introduction to numerical functional analysis with applications to the Ritz method along with the method of finite elements, the Galerkin methods, and the difference method. Many exercises complement the text. The theory of monotone operators is closely related to Hilbert's rigorous justification of the Dirichlet principle, and to the 19th and 20th problems of Hilbert which he formulated in his famous Paris lecture in 1900, and which strongly influenced the development of analysis in the twentieth century.

Keywords

Hilbert space calculus convergence differential equation functional analysis integral integral equation operator partial differential equation stability variational problem

Authors and affiliations

  • Eberhard Zeidler
    • 1
  1. 1.Max-Planck-Institut fuer Mathematik in den NaturwissenschaftenLeipzigGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4612-0985-0
  • Copyright Information Springer-Verlag New York Inc. 1990
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4612-6971-7
  • Online ISBN 978-1-4612-0985-0
  • About this book