An Introduction to Nonlinear Analysis: Theory is an overview of some
basic, important aspects of Nonlinear Analysis, with an emphasis on
those not included in the classical treatment of the field. Today
Nonlinear Analysis is a very prolific part of modern mathematical
analysis, with fascinating theory and many different applications
ranging from mathematical physics and engineering to social sciences and
economics. Topics covered in this book include the necessary background
material from topology, measure theory and functional analysis (Banach
space theory). The text also deals with multivalued analysis and basic
features of nonsmooth analysis, providing a solid background for the
more applications-oriented material of the book An Introduction to
Nonlinear Analysis: Applications by the same authors.
The book is self-contained and accessible to the newcomer, complete with
numerous examples, exercises and solutions. It is a valuable tool, not
only for specialists in the field interested in technical details, but
also for scientists entering Nonlinear Analysis in search of promising
directions for research.