Topological Degree Theory and Applications
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Topological Degree Theory and Applications

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Description

Since the 1960s, many researchers have extended topological degree theory to various non-compact type nonlinear mappings, and it has become a valuable tool in nonlinear analysis. Presenting a survey of advances made in generalizations of degree theory during the past decade, this book focuses on topological degree theory in normed spaces and its applications.

The authors begin by introducing the Brouwer degree theory in Rn, then consider the Leray-Schauder degree for compact mappings in normed spaces. Next, they explore the degree theory for condensing mappings, including applications to ODEs in Banach spaces. This is followed by a study of degree theory for A-proper mappings and its applications to semilinear operator equations with Fredholm mappings and periodic boundary value problems. The focus then turns to construction of Mawhin's coincidence degree for L-compact mappings, followed by a presentation of a degree theory for mappings of class (S+) and its perturbations with other monotone-type mappings. The final chapter studies the fixed point index theory in a cone of a Banach space and presents a notable new fixed point index for countably condensing maps.

Examples and exercises complement each chapter. With its blend of old and new techniques, Topological Degree Theory and Applications forms an outstanding text for self-study or special topics courses and a valuable reference for anyone working in differential equations, analysis, or topology.
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Product details

  • Hardback | 232 pages
  • 160 x 236.2 x 17.8mm | 453.6g
  • Chapman & Hall/CRC
  • Boca Raton, FL, United States
  • English
  • New.
  • 50 Illustrations, black and white
  • 158488648X
  • 9781584886488

Table of contents

BROUWER DEGREE THEORY
Continuous and Differentiable Functions
Construction of Brouwer Degree
Degree Theory for Functions in VMO
Applications to ODEs
Exercises

LERAY-SCHAUDER DEGREE THEORY
Compact Mappings
Leray-Schauder Degree
Leray-Schauder Degree for Multi-valued Mappings
Applications to Bifurcations
Applications to ODEs and PDEs
Exercises

DEGREE THEORY FOR SET CONTRACTIVE MAPS
Measure of Non-compactness and Set Contractions
Degree Theory for Countably Condensing Mappings
Applications to ODEs in Banach Spaces
Exercises

GENERALIZED DEGREE THEORY FOR A-PROPER MAPS
A-Proper Mappings
Generalized Degree for A-Proper Mappings
Equations with Fredholm Mappings of Index Zero
Equations with Fredholm Mappings of Index Zero Type
Applications of the Generalized Degree
Exercises

COINCIDENCE DEGREE THEORY
Fredholm Mappings
Coincidence Degree for L-Compact Mappings
Existence Theorems for Operator Equations
Applications to ODEs
Exercises

DEGREE THEORY FOR MONOTONE TYPE MAPS
Monotone Type Mappings in Reflexive Banach Spaces
Degree Theory for Mappings of Class (S+)
Degree for Perturbations of Monotone Type Mappings
Degree Theory for Mappings of Class (S+)L
Coincidence Degree for Mappings of Class L - (S+)
Computation of Topological Degree
Applications to PDEs and Evolution Equations
Exercises

FIXED POINT INDEX THEORY
Cone in Normed Spaces
Fixed Point Index Theory
Fixed Point Theorems in Cones
Perturbations of Condensing Mappings
Index Theory for Nonself-Mappings
Applications to Integral and Differential Equations
Exercises

REFERENCES
SUBJECT INDEX
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