Methods of Nonlinear Analysis: Applications to Differential Equations

Drabek P., Milota J.

In this book, fundamental methods of nonlinear analysis are introduced, discussed and illustrated in straightforward examples. Every method considered is motivated and explained in its general form, but presented in an abstract framework as comprehensively as possible. Applications and generalizations are shown. In particular, a large number of methods is applied to boundary value problems for partial differential equations. The text is structured in two levels: a self-contained basic level and an advanced level – organized in appendices – for the more experienced reader. It thus serves as both a textbook for graduate-level courses and a reference book for mathematicians, engineers and applied scientists.

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Table of contents :
Preface……Page 8
Contents……Page 6
1 Preliminaries……Page 12
2 Properties of Linear and Nonlinear Operators……Page 65
3 Abstract Integral and Differential Calculus……Page 114
4 Local Properties of Differentiable Mappings……Page 148
5 Topological and Monotonicity Methods……Page 258
6 Variational Methods……Page 369
7 Boundary Value Problems for Partial Differential Equations……Page 481
Summary of MethodsPresented in This Book……Page 541
Typical Applications……Page 543
Comparison of BifurcationResults Presented in This Book……Page 547
List of Symbols……Page 549
Index……Page 553
Bibliography……Page 568