Nikolaos S. Papageorgiou – författare

Accurate models to describe real-world phenomena are indispensable for research in such scientific fields as physics, engineering, biology, chemistry, and economics. The tools and techniques of applied analysis facilitate the development of mathematical models and can thereby serve as an excellent resource for students and researchers in various scientific and mathematical disciplines.

This self-contained, comprehensive handbook provides an in-depth examination of important theoretical methods and procedures in applied analysis.

Unique features of the Handbook of Applied Analysis:

• Presents an accessible introduction to modern analysis, while still serving as a useful reference for researchers and practitioners;

• Covers a large number of diverse topics: smooth and nonsmooth differential calculus, optimal control, fixed point theory, critical point theory, linear and nonlinear eigenvalue problems, nonlinear boundary value problems, set-valued analysis, game theory, stochastic analysis, and evolutionary equations;

• Serves as a complete guide to the theory of nonlinear analysis;

• Includes numerous examples that demonstrate and expand upon the topics presented;

• Suggests many directions for further research and study.

In this one volume, the reader can find many of the most important theoretical trends in nonlinear analysis and applications to different fields. These features, together with an extensive bibliography, make the volume a valuable tool for every researcher working on nonlinear 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. Today Nonlinear Analysis is a very prolific part of modern mathematical analysis, with fascinating theory and many different applications ranging from mathematical physics and engineering to social sciences and economics. Topics covered in this book include the necessary background material from topology, measure theory and functional analysis (Banach space theory). The text also deals with multivalued analysis and basic features of nonsmooth analysis, providing a solid background for the more applications-oriented material of the book An Introduction to Nonlinear Analysis: Applications by the same authors.

The book is self-contained and accessible to the newcomer, complete with numerous examples, exercises and solutions. It is a valuable tool, not only for specialists in the field interested in technical details, but also for scientists entering Nonlinear Analysis in search of promising directions for research.

This book emphasizes those basic abstract methods and theories that are useful in the study of nonlinear boundary value problems. The content is developed over six chapters, providing a thorough introduction to the techniques used in the variational and topological analysis of nonlinear boundary value problems described by stationary differential operators. The authors give a systematic treatment of the basic mathematical theory and constructive methods for these classes of nonlinear equations as well as their applications to various processes arising in the applied sciences. They show how these diverse topics are connected to other important parts of mathematics, including topology, functional analysis, mathematical physics, and potential theory. Throughout the book a nice balance is maintained between rigorous mathematics and physical applications. The primary readership includes graduate students and researchers in pure and applied nonlinear analysis.

This book, the second of two volumes, presents significant applications for understanding modern analysis. It empowers young researchers with key techniques and applications to explore various subfields of this broad subject and introduces relevant frameworks for immediate deployment.

The applications list begins with Degree Theory, a useful tool for studying nonlinear equations. Chapter 2 deals with Fixed Point Theory, and Chapter 3 introduces Critical Point Theory. Chapter 4 presents the main spectral properties of linear, nonlinear, anisotropic, and double-phase differential operators. Chapter 5 covers semilinear and nonlinear elliptic equations with different boundary conditions, while Chapter 6 addresses dynamic systems monitored by ordinary and partial differential equations. Chapter 7 delves into optimal control problems, and Chapter 8 discusses some economic models, providing a brief presentation of Game Theory and Nash equilibrium.

By offering a clear and comprehensive overview of modern analysis tools and applications, this work can greatly benefit mature graduate students seeking research topics, as well as experienced researchers interested in this vast and rich field of mathematics.

The aim of this book is to provide a concise but complete introduction to the main mathematical tools of nonlinear functional analysis, which are also used in the study of concrete problems in economics, engineering, and physics. This volume gathers the mathematical background needed in order to conduct research or to deal with theoretical problems and applications using the tools of nonlinear functional analysis.

Contents Basic Topology Measure Theory Basic Functional Analysis Banach Spaces of Functions and Measures Convex Functions – Nonsmooth Analysis Nonlinear Analysis