Methods of Nonlinear Analysis
Subtitle: Applications to Differential Equations
By: by Pavel Drábek, Jaroslav Milota
Contributors: Milota, Jaroslav; SpringerLink (Online service)
Edition: 2nd ed. 2013.
Series: Birkhäuser Advanced Texts Basler Lehrbücher
Publisher: Springer Basel; Imprint: Birkhäuser
Published: 2013
Place of publication: Basel
Language: eng
Format: [electronic resource] :
Number of pages: 649
ISBN-13: 9783034803878
Subjects: Partial Differential equations; Global analysis (Mathematics); Functional analysis; Mathematics; Mathematical optimization; Calculus of Variations and Optimal Control; Optimization; Analysis
Description: <p>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. </p><p>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.</p><p>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.  </p>
Table of contents: title: Preface; title: 1 Preliminaries; title: 2 Properties of Linear and Nonlinear Operators; title: 3 Abstract Integral and Differential Calculus; title: 4 Local Properties of Differentiable Mappings; title: 5 Topological and Monotonicity Methods; title: 6 Variational Methods; title: 7 Boundary Value Problems for Partial Differential Equations; title: Summary of Methods; title: Typical Applications; title: Comparison of Bifurcation Results; title: List of Symbols; title: Index; title: Bibliography.