Synopses & Reviews
Hailed as "eminently suitable as a text for a graduate course" by the
Bulletin of the American Mathematical Society, this volume offers a survey of the main ideas, concepts, and methods that constitute nonlinear functional analysis. It offers extensive commentary and many examples in addition to an abundance of interesting, challenging exercises.
Starting with coverage of the development of the Brower degree and its applications, the text proceeds to examinations of degree mappings for infinite dimensional spaces and surveys of monotone and accretive mappings. Subsequent chapters explore the inverse function theory, the implicit function theory, and Newton's methods as well as fixed-point theory, solutions to cones, and the Galerkin method of studying nonlinear equations. The final chapters address extremal problemsincluding convexity, Lagrange multipliers, and mini-max theoremsand offer an introduction into bifurcation theory. Suitable for graduate-level mathematics courses, this volume also serves as a reference for professionals.
Synopsis
This text offers a survey of the main ideas, concepts, and methods that constitute nonlinear functional analysis. It features extensive commentary, many examples, and interesting, challenging exercises. 1985 edition.
Synopsis
This text offers a survey of the main ideas, concepts, and methods that constitute nonlinear functional analysis. It features extensive commentary, many examples, and interesting, challenging exercises. 1985 edition.
Table of Contents
1. Topological Degree in Finite Dimensions2. Topological Degrees in Infinite Dimensions3. Monotone and Accretive Operators4. Implicit Functions and Problems in Resonance5. Fixed Point Theory6. Solutions in Cones7. Approximate Solutions8. Multis9. Extremal Problems10. BifurcationEpilogueBibliographySymbols Index