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Topological Degree Theory and Applications

Topological Degree Theory and Applications by Yeol Je Cho
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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
CRC Press; March 2006
228 pages; ISBN 9781420011487
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Title: Topological Degree Theory and Applications
Author: Yeol Je Cho; Yu-Qing Chen
 
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