Bücher von Nikolaos S. Papageorgiou

This book, which is the first of two volumes, presents, in a unique way, some of the most relevant research tools of modern analysis. This work empowers young researchers with all the necessary techniques to explore the various subfields of this broad subject, and introduces relevant frameworks where these tools can be immediately deployed.Volume I starts with the foundations of modern analysis. The first three chapters are devoted to topology, measure theory, and functional analysis. Chapter 4 offers a comprehensive analysis of the main function spaces, while Chapter 5 covers more concrete subjects, like multivariate analysis, which are closely related to applications and more difficult to find in compact form. Chapter 6 deals with smooth and non-smooth calculus of functions; Chapter 7 introduces certain important classes of nonlinear operators; and Chapter 8 complements the previous three chapters with topics of variational analysis. Each chapter of this volume finishes with a list of problems - handy for understanding and self-study - and historical notes that give the reader a more vivid picture of how the theory developed. Volume II consists of various applications using the tools and techniques developed in this volume.By offering a clear and wide picture of the tools and applications of modern analysis, this work can be of great benefit not only to mature graduate students seeking topics for research, but also to experienced researchers with an interest in this vast and rich field of mathematics.

In volume I we developed the tools of "e;Multivalued Analysis. "e; In this volume we examine the applications. After all, the initial impetus for the development of the theory of set-valued functions came from its applications in areas such as control theory and mathematical economics. In fact, the needs of control theory, in particular the study of systems with a priori feedback, led to the systematic investigation of differential equations with a multi valued vector field (differential inclusions). For this reason, we start this volume with three chapters devoted to set-valued differential equations. However, in contrast to the existing books on the subject (i. e. J. -P. Aubin - A. Cellina: "e;Differential Inclusions,"e; Springer-Verlag, 1983, and Deimling: "e;Multivalued Differential Equations,"e; W. De Gruyter, 1992), here we focus on "e;Evolution Inclusions,"e; which are evolution equations with multi- valued terms. Evolution equations were raised to prominence with the development of the linear semigroup theory by Hille and Yosida initially, with subsequent im- portant contributions by Kato, Phillips and Lions. This theory allowed a successful unified treatment of some apparently different classes of nonstationary linear par- tial differential equations and linear functional equations. The needs of dealing with applied problems and the natural tendency to extend the linear theory to the nonlinear case led to the development of the nonlinear semigroup theory, which became a very effective tool in the analysis of broad classes of nonlinear evolution equations.

This book emphasizes those basic abstract methods and theories that are useful in the study of nonlinear boundary value problems. They show how these diverse topics are connected to other important parts of mathematics, including topology, functional analysis, mathematical physics, and potential theory.

Exercises in Analysis will be published in two volumes. The entire collection of exercises offers a balanced and useful picture for the application surrounding each topic. This nearly encyclopedic coverage of exercises in mathematical analysis is the first of its kind and is accessible to a wide readership.

This second of two Exercises in Analysis volumes covers problems in five core topics of mathematical analysis: Function Spaces, Nonlinear and Multivalued Maps, Smooth and Nonsmooth Calculus, Degree Theory and Fixed Point Theory, and Variational and Topological Methods.

Although the presentation of the subject requires some knowledge in various areas of mathematical analysis, we have deliberately made this book more or less self-contained, with the help of an extended appendix in which we have gathered several basic notions and results from topology, measure theory and nonlinear functional analysis.

An Introduction to Nonlinear Analysis: Theory is an overview of some basic, important aspects of Nonlinear Analysis, with an emphasis on those not included in the classical treatment of the field.

This book offers an exposition of the main applications of Nonlinear Analysis, beginning with a chapter on Nonlinear Operators and Fixed Points, a connecting point and bridge from Nonlinear Analysis theory to its applications.

This book offers an exposition of the main applications of Nonlinear Analysis, beginning with a chapter on Nonlinear Operators and Fixed Points, a connecting point and bridge from Nonlinear Analysis theory to its applications.

An Introduction to Nonlinear Analysis: Theory is an overview of some basic, important aspects of Nonlinear Analysis, with an emphasis on those not included in the classical treatment of the field.

This self-contained, comprehensive handbook provides an in-depth examination of important theoretical methods and procedures in applied analysis. It includes numerous examples that demonstrate and expand upon the topics presented.