Topics in Nonlinear Functional Analysis (Courant Lecture Notes) - Softcover

Nirenberg, Louis

Softcover

ISBN 10: 0821828193 ISBN 13: 9780821828199

Publisher: Amer Mathematical Society, 2001

Synopsis

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.

Edition details

• Publisher: Amer Mathematical Society
• Publication date: 2001
• Language: English
• ISBN 10: 0821828193
• ISBN 13: 9780821828199
• Binding: Paperback
• Number of pages: 145