Theory of Degrees with Applications to Bifurcations and Differential Equations (Wiley-Interscience and Canadian Mathematics Series of Monographs and Texts)

This book provides an introduction to degree theory and its applications to nonlinear differential equations. It uses an applications-oriented approach to address functional analysis, general topology and differential equations and offers a unified treatment of the classical Brouwer degree, the recently developed S 1-degree and the Dold-Ulrich degree for equivalent mappings and bifurcation problems. It integrates two seemingly disparate concepts, beginning with review material before shifting to classical theory and advanced application techniques.Provides a detailed illustration of the power of the global bifurcation theorem in establishing large-amplitude periodic solutions.-- Uses figures and tables to illustrate the geometric meaning of complicated analysis.