Ebook: Nonlinear Functional Analysis - A First Course

The book discusses the basic theory of topological and variational methods used in solving nonlinear equations involving mappings between normed linear spaces. It is meant to be a primer of nonlinear analysis and is designed to be used as a text or reference book by graduate students. Frechet derivative, Brouwer fixed point theorem, Borsuk's theorem, and bifurcation theory along with their applications have been discussed. Several solved examples and exercises have been carefully selected and included in the present edition. The prerequisite for following this book is the basic knowledge of functional analysis and topology.
In the present second edition, the presentation has been completely overhauled
without changing the basic structure of the book. The statements of results, definitions
and remarks have been modified wherever necessary, and many proofs have been
rewritten, in view of greater clarity of the exposition. Some examples and exercises
have been added. A completely new section on monotone mappings has been added,
and the proofs of a few more important fixed point theorems have been included.