Kesavan S. Nonlinear Functional Analysis.A First Course 2ed 2022

Textbook in PDF format

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.
Preface to the Second Edition.
Preface to the First Edition.
Differential Calculus on Normed Linear Spaces.
The Brouwer Degree.
The Leray–Schauder Degree.
Bifurcation Theory.
Critical Points of Functionals.
Index