Methods of nonlinear analysis: applications to differential equations

Pavel Drabek, Jaroslav Milota9783764381462, 3764381469

In this book, the basic methods of nonlinear analysis are emphasized and illustrated in simple examples. Every considered method is motivated, explained in a general form but in the simplest possible abstract framework, and its applications are shown, particularly to boundary value problems for elementary ordinary or partial differential equations. The text is organized in two levels – a self-contained basic and, organized in appendices, an advanced level for the more experienced reader.

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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