An Introduction to Nonlinear Analysis: Applications

ISBN-13: 9780306474569 / Angielski / Twarda / 2003 / 823 str.

Zdisllaw Denkowski; Zdzisaw Denkowski; Stanislaw Migsrski

Opis

An Introduction to Nonlinear Analysis: Applications offers an exposition of the main applications of Nonlinear Analysis. Its starting point is a chapter on Nonlinear Operators and Fixed Points, a connecting point and bridge from Nonlinear Analysis theory to its applications. The topics covered include applications to ordinary and partial differential equations, optimization, optimal control, calculus of variations and mathematical economics. This book is an excellent springboard for anyone wishing to conduct advanced research or work on a postgraduate text. Many exercises and their solutions complement the presentation. The text is a companion to An Introduction to Nonlinear Analysis: Theory by the same authors.

Recenzje

From the reviews of the first edition:

"The book by Z. Denkowski, S. Migorski, and N. S. Papageorgiou is a valuable addition to the literature on the subject. We strongly recommend it as a rigorous, up-to-date text in the field."
(Sergiu Aizicovici, Ohio University)

"The book under review ... covers some applications of nonlinear analysis. ... This volume will be very useful for everybody whose research involves methods from nonlinear analysis. Overall this is a very interesting and well written book." (Tzanko D. Donchev, Mathematical Reviews, 2005 b)

"The monograph under review concentrates on the applications of nonlinear analysis ... . The monograph is enriched by many examples and applications to various problems, also of concrete type. ... Historical and bibliographical remarks concluding each chapter are very interesting and valuable. ... This monograph is well organized and clearly written. It is very useful for anyone who is interested in modern nonlinear analysis and its applications. It is ideal both as a text for a graduate-level class and as a reference for researchers." (S. Burys, Zentralblatt MATH, Vol. 1054 (5), 2005)

Spis treści

Applications:- List of Figures. Preface. 1. Nonlinear Operators and Fixed Points. 2. Ordinary Differential Equations. 3. Partial Differential Equations. 4. Optimal Control and Calculus of Variations. 5. Mathematical Economics. References. Index.