Methods of Nonlinear Analysis

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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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.

• Boundary value problem
• calculus
• differential equation
• functional analysis
• nonlinear analysis
• partial differential equation
• partial differential equations

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)

• 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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