Progress in Nonlinear Differential Equations and Their Applications

An Introduction to Nonlinear Functional Analysis and Elliptic Problems

Authors: Ambrosetti, Antonio, Arcoya Álvarez, David

  • Provides the basic, abstract tools used in nonlinear analysis
  • Presents key results such as the Banach contraction principle, a fixed point theorem for increasing operators, local and global inversion theory, Leray--Schauder degree, critical point theory, and bifurcation theory
  • Outlines a variety of approaches and displays how they can easily be applied to a range of model cases
  • Clear exposition driven by numerous prototype problems
  • An extensive appendix that includes further results on weak derivatives
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About this Textbook

This self-contained textbook provides the basic, abstract tools used in nonlinear analysis and their applications to semilinear elliptic boundary value problems. By first outlining the advantages and disadvantages of each method, this comprehensive text displays how various approaches can easily be applied to a range of model cases.

An Introduction to Nonlinear Functional Analysis and Elliptic Problems is divided into two parts: the first discusses key results such as the Banach contraction principle, a fixed point theorem for increasing operators, local and global inversion theory, Leray–Schauder degree, critical point theory, and bifurcation theory; the second part shows how these abstract results apply to Dirichlet elliptic boundary value problems.  The exposition is driven by numerous prototype problems and exposes a variety of approaches to solving them.

Complete with a preliminary chapter, an appendix that includes further results on weak derivatives, and chapter-by-chapter exercises, this book is a practical text for an introductory course or seminar on nonlinear functional analysis.

About the authors

Both authors are leading experts in this area of mathematics. Antonio Ambrosetti has been at the very forefront of research in this field for forty years, and several of the major topics from Parts 1 and 2 of the book are drawn from his research.

Reviews

From the reviews:

“The book is devoted to nonlinear functional analysis and its applications to semilinear elliptic boundary value problems. It covers a great variety of topics and gives a good introduction to the subject. … The book is aimed at graduate and senior undergraduate students.” (Alexander A. Pankov, Mathematical Reviews, Issue 2012 f)

“This book provides some basic abstract tools used in modern nonlinear analysis in strong relationship with their applications to semilinear elliptic boundary value problems. … This monograph is suitable for graduate students and researchers … . the volume under review should certainly be in the library of every university where research in mathematics is conducted.” (Vicenţiu D. Rădulescu, Zentralblatt MATH, Vol. 1228, 2012)


Table of contents (13 chapters)

  • Preliminaries

    Ambrosetti, Antonio (et al.)

    Pages 1-15

  • Some Fixed Point Theorems

    Ambrosetti, Antonio (et al.)

    Pages 17-21

  • Local and Global Inversion Theorems

    Ambrosetti, Antonio (et al.)

    Pages 23-31

  • Leray—Schauder Topological Degree

    Ambrosetti, Antonio (et al.)

    Pages 33-45

  • An Outline of Critical Points

    Ambrosetti, Antonio (et al.)

    Pages 47-60

Buy this book

eBook $54.99
price for USA (gross)
  • ISBN 978-0-8176-8114-2
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $69.99
price for USA
  • ISBN 978-0-8176-8113-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
An Introduction to Nonlinear Functional Analysis and Elliptic Problems
Authors
Series Title
Progress in Nonlinear Differential Equations and Their Applications
Series Volume
82
Copyright
2011
Publisher
Birkhäuser Basel
Copyright Holder
Springer Science+Business Media, LLC
eBook ISBN
978-0-8176-8114-2
DOI
10.1007/978-0-8176-8114-2
Hardcover ISBN
978-0-8176-8113-5
Series ISSN
1421-1750
Edition Number
1
Number of Pages
XII, 199
Number of Illustrations and Tables
12 b/w illustrations
Topics