Topological Analysis From the Basics to the Triple Degree for Nonlinear Fredholm Inclusions

The series is devoted to the publication of high-level monographs which cover the whole spectrum of current nonlinear analysis and applications in various fields, such as optimization, control theory, systems theory, mechanics, engineering, and other sciences. One of its main objectives is to make a...

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Hlavní autor:	Vath, Martin
Médium:	E-kniha Kniha
Jazyk:	angličtina
Vydáno:	Germany De Gruyter 2012 Walter de Gruyter GmbH
Vydání:	1
Edice:	De Gruyter Series in Nonlinear Analysis and Applications
Témata:	Algebraic topology Analysis Banach Manifold Degree Theory Fredholm Fredholm Maps Fredholm operators Function Triples Hahn-Banach Theorem Implicit Function Theorem Inverse Function Theorem Linear Functional Analysis MATHEMATICS / Functional Analysis MATHEMATICS / Geometry / General MATHEMATICS / Mathematical Analysis MATHEMATICS / Research MATHEMATICS / Topology Mathematics. Analysis Multivalued Map Multivalued Maps Nonlinear Analysis Nonlinear Functional Analysis Nonlinear Inclusion Separation Axiom Topological degree Topological spaces Topology Triple Degree Triple Degree Hahn-Banach Theorem Degree Theory Function Triples Separation Axiom Topology Nonlinear Analysis Nonlinear Inclusion Multivalued Map Fredholm Maps Analysis Banach Manifold Multivalued Maps Fredholm Nonlinear Functional Analysis Inverse Function Theorem Linear Functional Analysis Implicit Function Theorem
ISBN:	9783110277333, 3110277336, 9783110277227, 3110277220
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Intro -- Preface -- 1 Introduction -- I Topology and Multivalued Maps -- 2 Multivalued Maps -- 2.1 Notations for Multivalued Maps and Axioms -- 2.1.1 Notations -- 2.1.2 Axioms -- 2.2 Topological Notations and Basic Results -- 2.3 Separation Axioms -- 2.4 Upper Semicontinuous Multivalued Maps -- 2.5 Closed and Proper Maps -- 2.6 Coincidence Point Sets and Closed Graphs -- 3 Metric Spaces -- 3.1 Notations and Basic Results for Metric Spaces -- 3.2 Three Measures of Noncompactness -- 3.3 Condensing Maps -- 3.4 Convexity -- 3.5 Two Embedding Theorems for Metric Spaces -- 3.6 Some Old and New Extension Theorems for Metric Spaces -- 4 Spaces Defined by Extensions, Retractions, or Homotopies -- 4.1 AE and ANE Spaces -- 4.2 ANR and AR Spaces -- 4.3 Extension of Compact Maps and of Homotopies -- 4.4 UV8 and Rd Spaces and Homotopic Characterizations -- 5 Advanced Topological Tools -- 5.1 Some Covering Space Theory -- 5.2 A Glimpse on Dimension Theory -- 5.3 Vietoris Maps -- II Coincidence Degree for Fredholm Maps -- 6 Some Functional Analysis -- 6.1 Bounded Linear Operators and Projections -- 6.2 Linear Fredholm Operators -- 7 Orientation of Families of Linear Fredholm Operators -- 7.1 Orientation of a Linear Fredholm Operator -- 7.2 Orientation of a Continuous Family -- 7.3 Orientation of a Family in Banach Bundles -- 8 Some Nonlinear Analysis -- 8.1 The Pointwise Inverse and Implicit Function Theorems -- 8.2 Oriented Nonlinear Fredholm Maps -- 8.3 Oriented Fredholm Maps in Banach Manifolds -- 8.4 A Partial Implicit Function Theorem in Banach Manifolds -- 8.5 Transversal Submanifolds -- 8.6 Parameter-Dependent Transversality and Partial Submanifolds -- 8.7 Orientation on Submanifolds and on Partial Submanifolds -- 8.8 Existence of Transversal Submanifolds -- 8.9 Properness of Fredholm Maps -- 9 The Brouwer Degree -- 9.1 Finite-Dimensional Manifolds
9.2 Orientation of Continuous Maps and of Manifolds -- 9.3 The Cr Brouwer Degree -- 9.4 Uniqueness of the Brouwer Degree -- 9.5 Existence of the Brouwer Degree -- 9.6 Some Classical Applications of the Brouwer Degree -- 10 The Benevieri-Furi Degrees -- 10.1 Further Properties of the Brouwer Degree -- 10.2 The Benevieri-Furi C1 Degree -- 10.3 The Benevieri-Furi Coincidence Degree -- III Degree Theory for Function Triples -- 11 Function Triples -- 11.1 Function Triples and Their Equivalences -- 11.2 The Simplifier Property -- 11.3 Homotopies of Triples -- 11.4 Locally Normal Triples -- 12 The Degree for Finite-Dimensional Fredholm Triples -- 12.1 The Triple Variant of the Brouwer Degree -- 12.2 The Triple Variant of the Benevieri-Furi Degree -- 13 The Degree for Compact Fredholm Triples -- 13.1 The Leray-Schauder Triple Degree -- 13.2 The Leray-Schauder Coincidence Degree -- 13.3 Classical Applications of the Leray-Schauder Degree -- 14 The Degree for Noncompact Fredholm Triples -- 14.1 The Degree for Fredholm Triples with Fundamental Sets -- 14.2 Homotopic Tests for Fundamental Sets -- 14.3 The Degree for Fredholm Triples with Convex-fundamental Sets -- 14.4 Countably Condensing Triples -- 14.5 Classical Applications in the General Framework -- 14.6 A Sample Application for Boundary Value Problems -- Bibliography -- Index of Symbols -- Index
Chapter 5. Advanced Topological Tools
Chapter 8. Some Nonlinear Analysis
Index
Chapter 11. Function Triples
Chapter 1. Introduction
Preface
Chapter 9. The Brouwer Degree
Part II. Coincidence Degree for Fredholm Maps --
Chapter 12. The Degree for Finite-Dimensional Fredholm Triples
Part I. Topology and Multivalued Maps --
Chapter 4. Spaces Defined by Extensions, Retractions, or Homotopies
Chapter 7. Orientation of Families of Linear Fredholm Operators
Chapter 10. The Benevieri–Furi Degrees
Part III. Degree Theory for Function Triples --
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Chapter 13. The Degree for Compact Fredholm Triples
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Chapter 6. Some Functional Analysis
Chapter 14. The Degree for Noncompact Fredholm Triples
Contents
Frontmatter --
Chapter 2. Multivalued Maps
Chapter 3. Metric Spaces
Bibliography
Index of Symbols