Topological Degree Theory and Applications
Topological Degree Theory and Applications
Description
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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