Methods of Nonlinear Analysis

This book introduces fundamental methods of nonlinear analysis, illustrating them in straightforward examples. The revised new edition offers evolutionary equations and differential equations on manifolds, and presents more advanced material in appendices.

In this book, fundamental methods of nonlinear analysis are introduced, discussed and illustrated in straightforward examples. Each method considered is motivated and explained in its general form, but presented in an abstract framework as comprehensively as possible. A large number of methods are applied to boundary value problems for both ordinary and partial differential equations. In this edition we have made minor revisions, added new material and organized the content slightly differently.

In particular, we included evolutionary equations and differential equations on manifolds. The applications to partial differential equations follow every abstract framework of the method in question.

The text is structured in two levels: a self-contained basic level and an advanced level - organized in appendices - for the more experienced reader. The last chapter contains more involved material and can be skipped by those new to the field. This book serves as both a textbook for graduate-level courses and a reference book for mathematicians, engineers and applied scientists

Designed as a textbook for advanced undergraduate and graduate students and useful as a handbook for scientists and engineers Two level structure: basic level for the beginners and advanced one for more experienced reader Accessible to beginners by avoiding too many technical details and keeping key assertions simple Transparent and illustrative examples Exercises are an organic part of the exposition and accompany the reader throughout the book Includes supplementary material: sn.pub/extras

Contenu
Preface.- 1 Preliminaries.- 2 Properties of Linear and Nonlinear Operators.- 3 Abstract Integral and Differential Calculus.- 4 Local Properties of Differentiable Mappings.- 5 Topological and Monotonicity Methods.- 6 Variational Methods.- 7 Boundary Value Problems for Partial Differential Equations.- Summary of Methods.- Typical Applications.- Comparison of Bifurcation Results.- List of Symbols.- Index.- Bibliography.