商品簡介
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 Brouwer 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 problemsuincluding convexity, Lagrange multipliers, and mini-max theoremsuand offer an introduction into bifurcation theory. Suitable for graduate-level mathematics courses, this volume also serves as a reference for professionals.
Dover (2010) unabridged republication of the edition published by Springer-Verlag, Berlin and Heidelberg, 1985.
作者簡介
Klaus Deimling is a Professor of Mathematics at the University of Paderborn in Germany.
