Download or read book Nonlinear Functional Analysis written by Klaus Deimling and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 465 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Geometric Nonlinear Functional Analysis written by Yoav Benyamini and published by American Mathematical Soc.. This book was released on 2000 with total page 503 pages. Available in PDF, EPUB and Kindle. Book excerpt: A systematic study of geometric nonlinear functional analysis. The main theme is the study of uniformly continuous and Lipschitz functions between Banach spaces. This study leads to the classification of Banach spaces and of their important subsets in the uniform and Lipschitz categories.
Download or read book Topics in Nonlinear Functional Analysis written by L. Nirenberg and published by American Mathematical Soc.. This book was released on 2001 with total page 159 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since its first appearance as a set of lecture notes published by the Courant Institute in 1974, this book served as an introduction to various subjects in nonlinear functional analysis. The current edition is a reprint of these notes, with added bibliographic references. Topological and analytic methods are developed for treating nonlinear ordinary and partial differential equations. The first two chapters of the book introduce the notion of topological degree and develop its basic properties. These properties are used in later chapters in the discussion of bifurcation theory (the possible branching of solutions as parameters vary), including the proof of Rabinowitz global bifurcation theorem. Stability of the branches is also studied. The book concludes with a presentation of some generalized implicit function theorems of Nash-Moser type with applications to Kolmogorov-Arnold-Moser theory and to conjugacy problems. For more than 20 years, this book continues to be an excellent graduate level textbook and a useful supplementary course text. Titles in this series are copublished with the Courant Institute of Mathematical Sciences at New York University.
Download or read book An Introduction to Nonlinear Functional Analysis and Elliptic Problems written by Antonio Ambrosetti and published by Springer Science & Business Media. This book was released on 2011-07-19 with total page 203 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Linear and Nonlinear Functional Analysis with Applications written by Philippe G. Ciarlet and published by SIAM. This book was released on 2013-10-10 with total page 847 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Applied Nonlinear Functional Analysis written by Nikolaos S. Papageorgiou and published by Walter de Gruyter GmbH & Co KG. This book was released on 2024-07-01 with total page 1003 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Contributions to Nonlinear Functional Analysis written by Eduardo H. Zarantonello and published by Academic Press. This book was released on 2014-05-10 with total page 687 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contributions to Nonlinear Functional Analysis contains the proceedings of a Symposium on Nonlinear Functional Analysis, held in Madison, Wisconsin, on April 12-14, 1971, under the sponsorship of the University of Wisconsin's Mathematics Research Center. The symposium provided a forum for discussing various topics related to nonlinear functional analysis, from transversality in nonlinear eigenvalue problems to monotonicity methods in Hilbert spaces and some applications to nonlinear partial differential equations. Comprised of 15 chapters, this book begins by presenting an extension of Leray-Schauder degree and an application to a nonlinear elliptic boundary value problem. The discussion then turns to the use of degree theory to prove the existence of global continua of solutions of nonlinear eigenvalue problems; transversality in nonlinear eigenvalue problems; and how variational structure can be used to study some local questions in bifurcation theory. Subsequent chapters deal with the notion of monotone operators and monotonicity theory; a nonlinear version of the Hille-Yosida theorem; a version of the penalty method for the Navier-Stokes equations; and various types of weak solutions for minimizing problems in the spirit of duality theory for convex functionals. This monograph will be of interest to students and practitioners in the field of mathematics who want to learn more about nonlinear functional analysis.
Download or read book Spectral Theory and Nonlinear Functional Analysis written by Julian Lopez-Gomez and published by CRC Press. This book was released on 2001-03-28 with total page 281 pages. Available in PDF, EPUB and Kindle. Book excerpt: This Research Note addresses several pivotal problems in spectral theory and nonlinear functional analysis in connection with the analysis of the structure set of zeroes of a general class of nonlinear operators. Appealing to a broad audience, it contains many important contributions to linear algebra, linear functional analysis, nonlinear functional analysis, and topology. The author gives several applications of the abstract theory to reaction diffusion equations and systems. The results presented cover a thirty-year period and cut across a variety of mathematical fields.
Download or read book Nonlinear Functional Analysis written by Jacob T. Schwartz and published by CRC Press. This book was released on 1969 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A Primer of Nonlinear Analysis written by Antonio Ambrosetti and published by Cambridge University Press. This book was released on 1995-03-09 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an elementary and self-contained introduction to nonlinear functional analysis and its applications, especially in bifurcation theory.
Download or read book Nonlinear Functional Analysis written by S. Kesavan and published by Springer. This book was released on 2004-01-15 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Nonlinear Functional Analysis in Banach Spaces and Banach Algebras written by Aref Jeribi and published by CRC Press. This book was released on 2015-08-14 with total page 369 pages. Available in PDF, EPUB and Kindle. Book excerpt: Uncover the Useful Interactions of Fixed Point Theory with Topological StructuresNonlinear Functional Analysis in Banach Spaces and Banach Algebras: Fixed Point Theory under Weak Topology for Nonlinear Operators and Block Operator Matrices with Applications is the first book to tackle the topological fixed point theory for block operator matrices w
Download or read book Methods in Nonlinear Analysis written by Kung-Ching Chang and published by Springer Science & Business Media. This book was released on 2005-11-21 with total page 448 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Banach Space Theory written by Marián Fabian and published by Springer Science & Business Media. This book was released on 2011-02-04 with total page 820 pages. Available in PDF, EPUB and Kindle. Book excerpt: Banach spaces provide a framework for linear and nonlinear functional analysis, operator theory, abstract analysis, probability, optimization and other branches of mathematics. This book introduces the reader to linear functional analysis and to related parts of infinite-dimensional Banach space theory. Key Features: - Develops classical theory, including weak topologies, locally convex space, Schauder bases and compact operator theory - Covers Radon-Nikodým property, finite-dimensional spaces and local theory on tensor products - Contains sections on uniform homeomorphisms and non-linear theory, Rosenthal's L1 theorem, fixed points, and more - Includes information about further topics and directions of research and some open problems at the end of each chapter - Provides numerous exercises for practice The text is suitable for graduate courses or for independent study. Prerequisites include basic courses in calculus and linear. Researchers in functional analysis will also benefit for this book as it can serve as a reference book.
Download or read book An Introduction to Nonlinear Analysis written by Martin Schechter and published by Cambridge University Press. This book was released on 2004 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Delay Equations written by Odo Diekmann and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 547 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim here is to provide an introduction to the mathematical theory of infinite dimensional dynamical systems by focusing on a relatively simple - yet rich - class of examples, delay differential equations. This textbook contains detailed proofs and many exercises, intended both for self-study and for courses at graduate level, as well as a reference for basic results. As the subtitle indicates, this book is about concepts, ideas, results and methods from linear functional analysis, complex function theory, the qualitative theory of dynamical systems and nonlinear analysis. The book provides the reader with a working knowledge of applied functional analysis and dynamical systems.
Download or read book Nonlinear Functional Analysis and Its Applications written by E. Zeidler and published by Springer Science & Business Media. This book was released on 1989-12-11 with total page 498 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the second of a five-volume exposition of the main principles of nonlinear functional analysis and its applications to the natural sciences, economics, and numerical analysis. The presentation is self -contained and accessible to the nonspecialist. Part II concerns the theory of monotone operators. It is divided into two subvolumes, II/A and II/B, which form a unit. The present Part II/A is devoted to linear monotone operators. It serves as an elementary introduction to the modern functional analytic treatment of variational problems, integral equations, and partial differential equations of elliptic, parabolic and hyperbolic type. This book also represents an introduction to numerical functional analysis with applications to the Ritz method along with the method of finite elements, the Galerkin methods, and the difference method. Many exercises complement the text. The theory of monotone operators is closely related to Hilbert's rigorous justification of the Dirichlet principle, and to the 19th and 20th problems of Hilbert which he formulated in his famous Paris lecture in 1900, and which strongly influenced the development of analysis in the twentieth century.
