Topological Degree Theory and Applications (Mathematical Analysis and Applications Book 10) 1st Edition by Yeol Je Cho (PDF)

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.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐The applications are too trivial to justify the use of degree theory. Such an abstract topic as degree theory should be dealt with a lot more detail, with definitions clearly made, not mentioned casually, with examples of problems that cannot be solved by simpler methods, and with drawings. so that people will believe these abstractions. A true understanding would seek to motivate degree theory from such problems, the way the theory was created. Instead, this book seems to be a collection of notes about degree theory, with no motivating examples, and no justifying applications. There are enough poorly written Math books without this one.

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