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© 2013

Methods of Nonlinear Analysis

Applications to Differential Equations

  • Designed as a textbook for advanced undergraduate and graduate students and useful as a handbook for scientists and engineers

  • Two level structure: basic level for the beginners and advanced one for more experienced reader

  • Accessible to beginners by avoiding too many technical details and keeping key assertions simple

  • Transparent and illustrative examples

  • Exercises are an organic part of the exposition and accompany the reader throughout the book

Textbook

Part of the Birkhäuser Advanced Texts Basler Lehrbücher book series (BAT)

Table of contents

  1. Front Matter
    Pages i-x
  2. Pavel Drábek, Jaroslav Milota
    Pages 1-53
  3. Pavel Drábek, Jaroslav Milota
    Pages 55-107
  4. Pavel Drábek, Jaroslav Milota
    Pages 109-148
  5. Pavel Drábek, Jaroslav Milota
    Pages 149-241
  6. Pavel Drábek, Jaroslav Milota
    Pages 243-359
  7. Pavel Drábek, Jaroslav Milota
    Pages 361-433
  8. Pavel Drábek, Jaroslav Milota
    Pages 435-564
  9. Pavel Drábek, Jaroslav Milota
    Pages 565-607
  10. Back Matter
    Pages 609-649

About this book

Introduction

In this book, fundamental methods of nonlinear analysis are introduced, discussed and illustrated in straightforward examples. Each method considered is motivated and explained in its general form, but presented in an abstract framework as comprehensively as possible. A large number of methods are applied to boundary value problems for both ordinary and partial differential equations. In this edition we have made minor revisions, added new material and organized the content slightly differently.

In particular, we included evolutionary equations and differential equations on manifolds. The applications to partial differential equations follow every abstract framework of the method in question.

The text is structured in two levels: a self-contained basic level and an advanced level - organized in appendices - for the more experienced reader. The last chapter contains more involved material and can be skipped by those new to the field. This book serves as both a textbook for graduate-level courses and a reference book for mathematicians, engineers and applied scientists. 

Keywords

boundary value problem evolution equation functional analysis nonlinear analysis ordinary and partial differential equations topological methods variational methods

Authors and affiliations

  1. 1.Faculty of Applied Sciences, Department of MathematicsUniversity of West BohemiaPlzeňCzech Republic
  2. 2.Faculty of Information Technology, Department of Applied MathematicsCzech Technical UniversityPraha 6Czech Republic

Bibliographic information

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Reviews

From the reviews of the second edition:

“The book is sufficiently wide-ranging to offer a panorama over nonlinear analysis and its applications to differential equations, and, at the same time, sufficiently structured and organized in order to allow the reader to easily access a specific topic in this broad domain of mathematics. Certainly, undergraduate and graduate students, as well as researchers in pure and applied mathematics will find that the book is a useful field guide providing excellent motivation for study and inspiration for new contributions and applications.” (Radu Precup, Zentralblatt MATH, Vol. 1264, 2013)