Applied Nonlinear Analysis - (Dover Books on Mathematics) by Jean-Pierre Aubin & Ivar Ekeland (Paperback)

About the Book

This introductory text offers simple presentations of the fundamentals of nonlinear analysis, with direct proofs and clear applications. Topics include smooth/nonsmooth functions, convex/nonconvex variational problems, economics, and mechanics. 1984 edition.

Book Synopsis

Nonlinear analysis, formerly a subsidiary of linear analysis, has advanced as an individual discipline, with its own methods and applications. Moreover, students can now approach this highly active field without the preliminaries of linear analysis. As this text demonstrates, the concepts of nonlinear analysis are simple, their proofs direct, and their applications clear. No prerequisites are necessary beyond the elementary theory of Hilbert spaces; indeed, many of the most interesting results lie in Euclidean spaces.
In order to remain at an introductory level, this volume refrains from delving into technical difficulties and sophisticated results not in current use. Applications are explained as soon as possible, and theoretical aspects are geared toward practical use. Topics range from very smooth functions to nonsmooth ones, from convex variational problems to nonconvex ones, and from economics to mechanics. Background notes, comments, bibliography, and indexes supplement the text.

About the Author

Both authors are Professors of Mathematics at Paris-Dauphine University.