Description 
1 online resource (xii, 209 pages) 
Series 
Progress in nonlinear differential equations and their applications ; vol. 82 

Progress in nonlinear differential equations and their applications ; v. 82

Contents 
Notation  Preliminaries  Some Fixed Point Theorems  Local and Global Inversion Theorems  LeraySchauder Topological Degree  An Outline of Critical Points  Bifurcation Theory  Elliptic Problems and Functional Analysis  Problems with A Priori Bounds  Asymptotically Linear Problems  Asymmetric Nonlinearities  Superlinear Problems  Quasilinear Problems  Stationary States of Evolution Equations  Appendix A Sobolev Spaces  Exercises  Index  Bibliography 
Summary 
This selfcontained textbook provides the basic, abstract¡tools¡used in¡nonlinear analysis¡and their applications to semilinear elliptic boundary value problems.¡By first¡outlining the advantages and disadvantages of each method, this comprehensive text¡displays how various¡approaches¡can easily be¡applied¡to a range of model cases. An Introduction to Nonlinear Functional Analysis and Elliptic Problems¡is divided into two parts: the first discusses key¡results such as the Banach contraction principle, a fixed point theorem for increasing operators, local and global inversion theory, LeraySchauder degree, critical point theory, and bifurcation theory; the second part shows how these abstract results apply to Dirichlet elliptic boundary value problems.¡ The exposition is driven by numerous prototype problems and exposes a variety of approaches to¡solving them. Complete with a preliminary chapter, an appendix that includes further results on weak derivatives, and chapterbychapter exercises, this book is a¡practical text for an introductory course or seminar on nonlinear functional analysis 
Bibliography 
Includes bibliographical references (pages 193196) and index 
Subject 
Differential equations, Elliptic.


Nonlinear functional analysis.

Form 
Electronic book

Author 
Arcoya, David.

ISBN 
0817681140 (electronic bk.) 

9780817681142 (electronic bk.) 
