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.show more

Product details

  • Hardback | 232 pages
  • 160 x 236.2 x 17.8mm | 453.6g
  • Taylor & Francis Inc
  • Chapman & Hall/CRC
  • Boca Raton, FL, United States
  • English
  • New.
  • 50 black & white illustrations
  • 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 INDEXshow more