Download or read book Handbook of Multivalued Analysis written by Shouchuan Hu and published by Springer Science & Business Media. This book was released on 2013-11-21 with total page 941 pages. Available in PDF, EPUB and Kindle. Book excerpt: In volume I we developed the tools of "Multivalued Analysis. " 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: "Differential Inclusions," Springer-Verlag, 1983, and Deimling: "Multivalued Differential Equations," W. De Gruyter, 1992), here we focus on "Evolution Inclusions," 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.
Download or read book Handbook of Multivalued Analysis written by Shouchuan Hu and published by Springer. This book was released on 1997-10-31 with total page 968 pages. Available in PDF, EPUB and Kindle. Book excerpt: the many different applications that this theory provides. We mention that the existing literature on this subject includes the books of J. P. Aubin, J. P. Aubin-A. Cellina, J. P. Aubin-H. Frankowska, C. Castaing-M. Valadier, K. Deimling, M. Kisielewicz and E. Klein-A. Thompson. However, these books either deal with one particular domain of the subject or present primarily the finite dimensional aspects of the theory. In this volume, we have tried very hard to give a much more complete picture of the subject, to include some important new developments that occurred in recent years and a detailed bibliography. 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. In this volume we present the theory of the subject, while in the second volume we will discuss mainly applications. This volume is divided into eight chapters. The flow of chapters follows more or less the historical development of the subject. We start with the topological theory, followed by the measurability study of multifunctions. Chapter 3 deals with the theory of monotone and accretive operators. The closely related topics of the degree theory and fixed points of multifunctions are presented in Chapters 4 and 5, respectively.
Download or read book HU MULTIVALUED ANALYSIS SET written by Shouchuan Hu and published by Springer. This book was released on 2000-01-01 with total page 964 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Handbook of Multivalued Analysis written by Shouchuan Hu and published by Springer. This book was released on 1997-10-31 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: the many different applications that this theory provides. We mention that the existing literature on this subject includes the books of J. P. Aubin, J. P. Aubin-A. Cellina, J. P. Aubin-H. Frankowska, C. Castaing-M. Valadier, K. Deimling, M. Kisielewicz and E. Klein-A. Thompson. However, these books either deal with one particular domain of the subject or present primarily the finite dimensional aspects of the theory. In this volume, we have tried very hard to give a much more complete picture of the subject, to include some important new developments that occurred in recent years and a detailed bibliography. 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. In this volume we present the theory of the subject, while in the second volume we will discuss mainly applications. This volume is divided into eight chapters. The flow of chapters follows more or less the historical development of the subject. We start with the topological theory, followed by the measurability study of multifunctions. Chapter 3 deals with the theory of monotone and accretive operators. The closely related topics of the degree theory and fixed points of multifunctions are presented in Chapters 4 and 5, respectively.
Download or read book Handbook of Applied Analysis written by Nikolaos S. Papageorgiou and published by Springer Science & Business Media. This book was released on 2009-05-31 with total page 804 pages. Available in PDF, EPUB and Kindle. Book excerpt: This handbook provides an in-depth examination of important theoretical methods and procedures in applied analysis. It details many of the most important theoretical trends in nonlinear analysis and applications to different fields. These features make the volume a valuable tool for every researcher working on nonlinear analysis.
Download or read book Set Valued Mappings with Applications in Nonlinear Analysis written by Donal O'Regan and published by CRC Press. This book was released on 2002-09-26 with total page 498 pages. Available in PDF, EPUB and Kindle. Book excerpt: Interest in the mathematical analysis of multi-functions has increased rapidly over the past thirty years, partly because of its applications in fields such as biology, control theory and optimization, economics, game theory, and physics. Set Valued Mappings with Applications to Nonlinear Analysis contains 29 research articles from leading mathematicians in this area. The contributors were invited to submit papers on topics such as integral inclusion, ordinary and partial differential inclusions, fixed point theorems, boundary value problems, and optimal control. This collection will be of interest to researchers in analysis and will pave the way for the creation of new mathematics in the future.
Download or read book Some resuts on multivalued analysis their applications written by Nguyen Xuan Tan and published by . This book was released on 1982 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Multi Valued Variational Inequalities and Inclusions written by Siegfried Carl and published by Springer Nature. This book was released on 2021-03-02 with total page 596 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on a large class of multi-valued variational differential inequalities and inclusions of stationary and evolutionary types with constraints reflected by subdifferentials of convex functionals. Its main goal is to provide a systematic, unified, and relatively self-contained exposition of existence, comparison and enclosure principles, together with other qualitative properties of multi-valued variational inequalities and inclusions. The problems under consideration are studied in different function spaces such as Sobolev spaces, Orlicz-Sobolev spaces, Sobolev spaces with variable exponents, and Beppo-Levi spaces. A general and comprehensive sub-supersolution method (lattice method) is developed for both stationary and evolutionary multi-valued variational inequalities, which preserves the characteristic features of the commonly known sub-supersolution method for single-valued, quasilinear elliptic and parabolic problems. This method provides a powerful tool for studying existence and enclosure properties of solutions when the coercivity of the problems under consideration fails. It can also be used to investigate qualitative properties such as the multiplicity and location of solutions or the existence of extremal solutions. This is the first in-depth treatise on the sub-supersolution (lattice) method for multi-valued variational inequalities without any variational structures, together with related topics. The choice of the included materials and their organization in the book also makes it useful and accessible to a large audience consisting of graduate students and researchers in various areas of Mathematical Analysis and Theoretical Physics.
Download or read book Multivalued Maps And Differential Inclusions Elements Of Theory And Applications written by Valeri Obukhovskii and published by World Scientific. This book was released on 2020-04-04 with total page 221 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of multivalued maps and the theory of differential inclusions are closely connected and intensively developing branches of contemporary mathematics. They have effective and interesting applications in control theory, optimization, calculus of variations, non-smooth and convex analysis, game theory, mathematical economics and in other fields.This book presents a user-friendly and self-contained introduction to both subjects. It is aimed at 'beginners', starting with students of senior courses. The book will be useful both for readers whose interests lie in the sphere of pure mathematics, as well as for those who are involved in applicable aspects of the theory. In Chapter 0, basic definitions and fundamental results in topology are collected. Chapter 1 begins with examples showing how naturally the idea of a multivalued map arises in diverse areas of mathematics, continues with the description of a variety of properties of multivalued maps and finishes with measurable multivalued functions. Chapter 2 is devoted to the theory of fixed points of multivalued maps. The whole of Chapter 3 focuses on the study of differential inclusions and their applications in control theory. The subject of last Chapter 4 is the applications in dynamical systems, game theory, and mathematical economics.The book is completed with the bibliographic commentaries and additions containing the exposition related both to the sections described in the book and to those which left outside its framework. The extensive bibliography (including more than 400 items) leads from basic works to recent studies.
Download or read book Topological Fixed Point Theory of Multivalued Mappings written by Lech Górniewicz and published by Springer Science & Business Media. This book was released on 2006-06-03 with total page 548 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to the topological fixed point theory of multivalued mappings including applications to differential inclusions and mathematical economy. It is the first monograph dealing with the fixed point theory of multivalued mappings in metric ANR spaces. Although the theoretical material was tendentiously selected with respect to applications, the text is self-contained. Current results are presented.
Download or read book Proceedings of the Conference on Differential Difference Equations and Applications written by Ravi P. Agarwal and published by Hindawi Publishing Corporation. This book was released on 2006 with total page 1266 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Some results on multivalued analysis and their applications written by Xuan-Tan Nguyen and published by . This book was released on 1982 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Exercises in Analysis written by Leszek Gasiński and published by Springer. This book was released on 2016-05-03 with total page 1069 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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. Each of five topics corresponds to a different chapter with inclusion of the basic theory and accompanying main definitions and results,followed by suitable comments and remarks for better understanding of the material. Exercises/problems are presented for each topic, with solutions available at the end of each chapter. 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. Graduate students will find the collection of problems valuable in preparation for their preliminary or qualifying exams as well as for testing their deeper understanding of the material. Exercises are denoted by degree of difficulty. Instructors teaching courses that include one or all of the above-mentioned topics will find the exercises of great help in course preparation. Researchers in analysis may find this Work useful as a summary of analytic theories published in one accessible volume.
Download or read book Handbook of Multivalued Analysis written by Shouchuan Hu and published by Springer. This book was released on 2013-12-06 with total page 932 pages. Available in PDF, EPUB and Kindle. Book excerpt: In volume I we developed the tools of "Multivalued Analysis. " 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: "Differential Inclusions," Springer-Verlag, 1983, and Deimling: "Multivalued Differential Equations," W. De Gruyter, 1992), here we focus on "Evolution Inclusions," 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.
Download or read book Applied Analysis and Differential Equations written by Ovidiu Carja and published by World Scientific. This book was released on 2007 with total page 363 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains refereed research articles written by experts in the field of applied analysis, differential equations and related topics. Well-known leading mathematicians worldwide and prominent young scientists cover a diverse range of topics, including the most exciting recent developments. A broad range of topics of recent interest are treated: existence, uniqueness, viability, asymptotic stability, viscosity solutions, controllability and numerical analysis for ODE, PDE and stochastic equations. The scope of the book is wide, ranging from pure mathematics to various applied fields such as classical mechanics, biomedicine, and population dynamics.
Download or read book Handbook of Complex Analysis written by Steven G. Krantz and published by CRC Press. This book was released on 2022-03-07 with total page 547 pages. Available in PDF, EPUB and Kindle. Book excerpt: In spite of being nearly 500 years old, the subject of complex analysis is still today a vital and active part of mathematics. There are important applications in physics, engineering, and other aspects of technology. This Handbook presents contributed chapters by prominent mathematicians, including the new generation of researchers. More than a compilation of recent results, this book offers students an essential stepping-stone to gain an entry into the research life of complex analysis. Classes and seminars play a role in this process. More, though, is needed for further study. This Handbook will play that role. This book is also a reference and a source of inspiration for more seasoned mathematicians—both specialists in complex analysis and others who want to acquaint themselves with current modes of thought. The chapters in this volume are authored by leading experts and gifted expositors. They are carefully crafted presentations of diverse aspects of the field, formulated for a broad and diverse audience. This volume is a touchstone for current ideas in the broadly construed subject area of complex analysis. It should enrich the literature and point in some new directions.
Download or read book Atomicity through Fractal Measure Theory written by Alina Gavriluţ and published by Springer Nature. This book was released on 2019-11-02 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents an exhaustive study of atomicity from a mathematics perspective in the framework of multi-valued non-additive measure theory. Applications to quantum physics and, more generally, to the fractal theory of the motion, are highlighted. The study details the atomicity problem through key concepts, such as the atom/pseudoatom, atomic/nonatomic measures, and different types of non-additive set-valued multifunctions. Additionally, applications of these concepts are brought to light in the study of the dynamics of complex systems. The first chapter prepares the basics for the next chapters. In the last chapter, applications of atomicity in quantum physics are developed and new concepts, such as the fractal atom are introduced. The mathematical perspective is presented first and the discussion moves on to connect measure theory and quantum physics through quantum measure theory. New avenues of research, such as fractal/multifractal measure theory with potential applications in life sciences, are opened.
