An Introduction to Nonlinear Functional Analysis and Elliptic Problems

An Introduction to Nonlinear Functional Analysis and Elliptic Problems
Author :
Publisher : Springer Science & Business Media
Total Pages : 203
Release :
ISBN-10 : 9780817681142
ISBN-13 : 0817681140
Rating : 4/5 (42 Downloads)

Synopsis An Introduction to Nonlinear Functional Analysis and Elliptic Problems by : Antonio Ambrosetti

This self-contained textbook provides the basic, abstract tools used in nonlinear analysis and their applications to semilinear elliptic boundary value problems and displays how various approaches can easily be applied to a range of model cases. Complete with a preliminary chapter, an appendix that includes further results on weak derivatives, and chapter-by-chapter exercises, this book is a practical text for an introductory course or seminar on nonlinear functional analysis.

An Introduction to Nonlinear Analysis

An Introduction to Nonlinear Analysis
Author :
Publisher : Cambridge University Press
Total Pages : 380
Release :
ISBN-10 : 0521843979
ISBN-13 : 9780521843973
Rating : 4/5 (79 Downloads)

Synopsis An Introduction to Nonlinear Analysis by : Martin Schechter

The techniques that can be used to solve non-linear problems are far different than those that are used to solve linear problems. Many courses in analysis and applied mathematics attack linear cases simply because they are easier to solve and do not require a large theoretical background in order to approach them. Professor Schechter's 2005 book is devoted to non-linear methods using the least background material possible and the simplest linear techniques. An understanding of the tools for solving non-linear problems is developed whilst demonstrating their application to problems in one dimension and then leading to higher dimensions. The reader is guided using simple exposition and proof, assuming a minimal set of pre-requisites. For completion, a set of appendices covering essential basics in functional analysis and metric spaces is included, making this ideal as an accompanying text on an upper-undergraduate or graduate course, or even for self-study.

An Introduction to Nonlinear Analysis: Applications

An Introduction to Nonlinear Analysis: Applications
Author :
Publisher : Springer Science & Business Media
Total Pages : 844
Release :
ISBN-10 : 0306474565
ISBN-13 : 9780306474569
Rating : 4/5 (65 Downloads)

Synopsis An Introduction to Nonlinear Analysis: Applications by : Zdzislaw Denkowski

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. The topics covered include applications to ordinary and partial differential equations, optimization, optimal control, calculus of variations and mathematical economics. The presentation is supplemented with the inclusion of many exercises and their solutions.

Optima and Equilibria

Optima and Equilibria
Author :
Publisher : Springer Science & Business Media
Total Pages : 442
Release :
ISBN-10 : 9783662035399
ISBN-13 : 3662035391
Rating : 4/5 (99 Downloads)

Synopsis Optima and Equilibria by : Jean-Pierre Aubin

Progress in the theory of economic equilibria and in game theory has proceeded hand in hand with that of the mathematical tools used in the field, namely nonlinear analysis and, in particular, convex analysis. Jean-Pierre Aubin, one of the leading specialists in nonlinear analysis and its application to economics, has written a rigorous and concise - yet still elementary and self-contained - textbook providing the mathematical tools needed to study optima and equilibria, as solutions to problems, arising in economics, management sciences, operations research, cooperative and non-cooperative games, fuzzy games etc. It begins with the foundations of optimization theory, and mathematical programming, and in particular convex and nonsmooth analysis. Nonlinear analysis is then presented, first game-theoretically, then in the framework of set valued analysis. These results are then applied to the main classes of economic equilibria. The book contains numerous exercises and problems: the latter allow the reader to venture into areas of nonlinear analysis that lie beyond the scope of the book and of most graduate courses.

Applied Nonlinear Functional Analysis

Applied Nonlinear Functional Analysis
Author :
Publisher : Walter de Gruyter GmbH & Co KG
Total Pages : 1003
Release :
ISBN-10 : 9783111288321
ISBN-13 : 3111288323
Rating : 4/5 (21 Downloads)

Synopsis Applied Nonlinear Functional Analysis by : Nikolaos S. Papageorgiou

The second edition covers the 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. The new edition includes some new topics on Banach spaces of functions and measures and nonlinear analysis.

Methods in Nonlinear Analysis

Methods in Nonlinear Analysis
Author :
Publisher : Springer Science & Business Media
Total Pages : 448
Release :
ISBN-10 : 9783540292326
ISBN-13 : 3540292322
Rating : 4/5 (26 Downloads)

Synopsis Methods in Nonlinear Analysis by : Kung-Ching Chang

This book offers a systematic presentation of up-to-date material scattered throughout the literature from the methodology point of view. It reviews the basic theories and methods, with many interesting problems in partial and ordinary differential equations, differential geometry and mathematical physics as applications, and provides the necessary preparation for almost all important aspects in contemporary studies. All methods are illustrated by carefully chosen examples from mechanics, physics, engineering and geometry.

KKM Theory and Applications in Nonlinear Analysis

KKM Theory and Applications in Nonlinear Analysis
Author :
Publisher : CRC Press
Total Pages : 648
Release :
ISBN-10 : 0824700317
ISBN-13 : 9780824700317
Rating : 4/5 (17 Downloads)

Synopsis KKM Theory and Applications in Nonlinear Analysis by : George Xian-Zhi Yuan

This reference provides a lucid introduction to the principles and applications of Knaster-Kuratowski-Mazurkiewicz (KKM) theory and explores related topics in nonlinear set-valued analysis.

Nonlinear Functional Analysis

Nonlinear Functional Analysis
Author :
Publisher : Springer Science & Business Media
Total Pages : 465
Release :
ISBN-10 : 9783662005477
ISBN-13 : 3662005476
Rating : 4/5 (77 Downloads)

Synopsis Nonlinear Functional Analysis by : Klaus Deimling

topics. However, only a modest preliminary knowledge is needed. In the first chapter, where we introduce an important topological concept, the so-called topological degree for continuous maps from subsets ofRn into Rn, you need not know anything about functional analysis. Starting with Chapter 2, where infinite dimensions first appear, one should be familiar with the essential step of consider ing a sequence or a function of some sort as a point in the corresponding vector space of all such sequences or functions, whenever this abstraction is worthwhile. One should also work out the things which are proved in § 7 and accept certain basic principles of linear functional analysis quoted there for easier references, until they are applied in later chapters. In other words, even the 'completely linear' sections which we have included for your convenience serve only as a vehicle for progress in nonlinearity. Another point that makes the text introductory is the use of an essentially uniform mathematical language and way of thinking, one which is no doubt familiar from elementary lectures in analysis that did not worry much about its connections with algebra and topology. Of course we shall use some elementary topological concepts, which may be new, but in fact only a few remarks here and there pertain to algebraic or differential topological concepts and methods.

Linear and Nonlinear Functional Analysis with Applications

Linear and Nonlinear Functional Analysis with Applications
Author :
Publisher : SIAM
Total Pages : 847
Release :
ISBN-10 : 9781611972580
ISBN-13 : 1611972582
Rating : 4/5 (80 Downloads)

Synopsis Linear and Nonlinear Functional Analysis with Applications by : Philippe G. Ciarlet

This single-volume textbook covers the fundamentals of linear and nonlinear functional analysis, illustrating most of the basic theorems with numerous applications to linear and nonlinear partial differential equations and to selected topics from numerical analysis and optimization theory. This book has pedagogical appeal because it features self-contained and complete proofs of most of the theorems, some of which are not always easy to locate in the literature or are difficult to reconstitute. It also offers 401 problems and 52 figures, plus historical notes and many original references that provide an idea of the genesis of the important results, and it covers most of the core topics from functional analysis.

Nonlinear Analysis

Nonlinear Analysis
Author :
Publisher : CRC Press
Total Pages : 992
Release :
ISBN-10 : 1584884843
ISBN-13 : 9781584884842
Rating : 4/5 (43 Downloads)

Synopsis Nonlinear Analysis by : Leszek Gasinski

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.