Methods of Nonlinear Analysis

- Preface

1. Preliminaries

2. Linear and Nonlinear Operators

3. Abstract Integral and Differential Calculus

4. Local Properties of Differentiable Mappings

5. Topological and Monotonicity Methods

6. Variational Methods

7. Boundary Value Problems for PDE

- Summary of Methods

- Typical Applications

- Comparison of Bifurcation Results

- Bibliography

- Index

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." (Vicentiu D. Radulescu, 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)