Nonlinear analysis is a broad, interdisciplinary field characterized by a remarkable mixture of analysis, topology, and applications. Its concepts and techniques provide the tools for developing more realistic and accurate models for a variety of phenomena encountered in fields ranging from engineering and chemistry to economics and biology.
This volume focuses on topics in nonlinear analysis pertinent to the theory of boundary value problems and their application in areas such as control theory and the calculus of variations. It complements the many other books on nonlinear analysis by addressing topics previously discussed fully only in scattered research papers. These include recent results on critical point theory, nonlinear differential operators, and related regularity and comparison principles.
The rich variety of topics, both theoretical and applied, make Nonlinear Analysis useful to anyone, whether graduate student or researcher, working in analysis or its applications in optimal control, theoretical mechanics, or dynamical systems. An appendix contains all of the background material needed, and a detailed bibliography forms a guide for further study.
Table of Contents
Hausdorff Measures and Capacity. Lebesgue-Bochner and Sobolev Spaces. Nonlinear Operators and Young Measures. Smooth and Nonsmooth Analysis and Variational Principles. Critical Point Theory. Eigenvalue Problems and Maximum Principles. Fixed Point Theory.
“This volume focuses on topics of nonlinear analysis related to the analysis of boundary value problems, control theory and the calculus of variations. It is mostly self-contained and, at the same time, it contains an impressive amount of material organized in 7 chapters – each of which, without being exhaustive, surveys and area of nonlinear analysis, starting with a brief introduction and finishing with historical comments. At the end of the book, there is an appendix containing basic results on topology, measure theory and functional analysis. Each chapter, which could have been a book by its own, moves rapidly from elementary definitions to involved results and generally presumes a degree of familiarity with the subject or requires a certain level of mathematical maturity. … this volume can be highly appreciated by readers without a pure theoretical background and orientation. Here on can find results previously contained only in scattered papers, not always easily accessible. … The reader might also find extremely useful the index table at the end … It may serve as a valuable reference text for active researchers in the area of nonlinear analysis and/or partial differential equations treated with variational techniques.”
— Aris Daniilidis, in Zentralblatt MATH, Vol. 1086, 2006/12
“The text is clearly and , in general, carefully written. This book is useful for researchers and parts of it can be recommended as additional reading for postgraduate students.”