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Methods of Nonlinear Analysis

Applications to Differential Equations

  • Textbook
  • © 2007

Overview

Authors:
  1. Pavel Drábek

    1. Department of Mathematics Faculty of Applied Sciences, University of West Bohemia in Pilsen, Plzeň, Czech Republic

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    You can also search for this author in PubMed   Google Scholar

  2. Jaroslav Milota

    1. Department of Mathematical Analysis Faculty of Mathematics and Physics, Charles University in Prague, Praha, Czech Republic

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    You can also search for this author in PubMed   Google Scholar

  • Designed as textbook for advanced undergraduate and graduate students and useful as handbook of nonlinear methods for scientists and engineers
  • Exercises are an organic part of the exposition, accompanying the reader throughout the book
  • Accessible to beginners by avoiding too many technical details and keeping key assertions simple
  • Includes supplementary material: sn.pub/extras

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

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Table of contents (7 chapters)

  1. Front Matter

    Pages i-xii
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  2. Preliminaries

    Pages 1-53

  3. Properties of Linear and Nonlinear Operators

    Pages 55-103

  4. Abstract Integral and Differential Calculus

    Pages 105-138

  5. Local Properties of Differentiable Mappings

    Pages 139-248

  6. Topological and Monotonicity Methods

    Pages 249-359

  7. Variational Methods

    Pages 361-472

  8. Boundary Value Problems for Partial Differential Equations

    Pages 473-532

  9. Back Matter

    Pages 533-568
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Keywords

About this book

In this book, the basic methods of nonlinear analysis are emphasized and illustrated in simple examples. Every considered method is motivated, explained in a general form but in the simplest possible abstract framework, and its applications are shown, particularly to boundary value problems for elementary ordinary or partial differential equations. The text is organized in two levels - a self-contained basic and, organized in appendices, an advanced level for the more experienced reader.

Reviews

From the reviews:

“This monograph contains old and new basic results from a significant part of the modern Nonlinear Analysis. … The book is well written and contains a wealth of material. … The book is carefully written, the style is informal, and the arguments are clear. It is a delightful read. … This book is recommended to researchers in Applied Mathematics who study various linear and nonlinear phenomena but it may be also useful and comprehensive for a broader community of mathematicians, physicists, and engineers.” (Vicenţiu D. Rădulescu, Zentralblatt MATH, Vol. 1176, 2010)

“The book covers a number of important methods in nonlinear analysis on a graduate level. … Each chapter consists of a self-contained introduction and ends with a number of appendices treating more advanced topics. The intention of the authors is to provide a well-motivated introduction to these topics and to demonstrate the usefulness of the derived methods in nontrivial applications, a task in which they succeed remarkably well.” (M. Kunzinger, Monatshefte für Mathematik, Vol. 157 (2), June, 2009)

“This book offers a self-contained introduction to certain central topics of functional analysis and topology for advanced undergraduate and graduate students. … the clear and self-contained style recommend the book for self-study, offering a quick introduction to a number of central notions of functional analysis and topology. A large number of exercises and historical remarks add to the pleasant overall impression the book leaves.” (M. Kunzinger, Monatshefte für Mathematik, Vol. 156 (3), March, 2009)

Authors and Affiliations

  • Department of Mathematics Faculty of Applied Sciences, University of West Bohemia in Pilsen, Plzeň, Czech Republic

    Pavel Drábek

  • Department of Mathematical Analysis Faculty of Mathematics and Physics, Charles University in Prague, Praha, Czech Republic

    Jaroslav Milota

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