Methods of Nonlinear Analysis
Applications to Differential Equations
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Beschreibung
In this book, fundamental methods of nonlinear analysis are introduced, discussed and illustrated in straightforward examples. Every method considered is motivated and explained in its general form, but presented in an abstract framework as comprehensively as possible. Applications and generalizations are shown. In particular, a large number of methods is applied to boundary value problems for partial differential equations.
The text is structured in two levels: a self-contained basic level and an advanced level - organized in appendices - for the more experienced reader. It thus serves as both a textbook for graduate-level courses and a reference book for mathematicians, engineers and applied scientists.
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. 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. Exercises are an organic part of the exposition and accompany the reader throughout the book. It is an ideal textbook for advanced undergraduate and graduate students as well as a useful handbook of nonlinear methods for scientists and engineers.
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
Autor*in
Pavel Drabek
Themen in »Methods of Nonlinear Analysis«
Boundary value problem calculus differential equation functional analysis nonlinear analysis partial differential equation partial differential equations
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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)
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