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Topics in Nonlinear Functional Analysis (Paperback)
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Topics in Nonlinear Functional Analysis (Paperback)
Series: Courant Lecture Notes
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Since its first appearance as a set of lecture notes published by
the Courant Institute in 1974, this book served as an introduction
to various subjects in nonlinear functional analysis. The current
edition is a reprint of these notes, with added bibliographic
references. Topological and analytic methods are developed for
treating nonlinear ordinary and partial differential equations. The
first two chapters of the book introduce the notion of topological
degree and develop its basic properties. These properties are used
in later chapters in the discussion of bifurcation theory (the
possible branching of solutions as parameters vary), including the
proof of Rabinowitz's global bifurcation theorem. Stability of the
branches is also studied.The book concludes with a presentation of
some generalized implicit function theorems of Nash-Moser type with
applications to Kolmogorov-Arnold-Moser theory and to conjugacy
problems. After more than 20 years, this book continues to be an
excellent graduate level textbook and a useful supplementary course
text.
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