Nonlinear Functional Analysis

  • Klaus Deimling

Table of contents

  1. Front Matter
    Pages I-XIV
  2. Klaus Deimling
    Pages 1-34
  3. Klaus Deimling
    Pages 35-94
  4. Klaus Deimling
    Pages 95-145
  5. Klaus Deimling
    Pages 146-185
  6. Klaus Deimling
    Pages 186-216
  7. Klaus Deimling
    Pages 217-255
  8. Klaus Deimling
    Pages 256-277
  9. Klaus Deimling
    Pages 278-318
  10. Klaus Deimling
    Pages 319-377
  11. Klaus Deimling
    Pages 378-425
  12. Klaus Deimling
    Pages 426-427
  13. Back Matter
    Pages 428-452

About this book

Introduction

topics. However, only a modest preliminary knowledge is needed. In the first chapter, where we introduce an important topological concept, the so-called topological degree for continuous maps from subsets ofRn into Rn, you need not know anything about functional analysis. Starting with Chapter 2, where infinite dimensions first appear, one should be familiar with the essential step of consider­ ing a sequence or a function of some sort as a point in the corresponding vector space of all such sequences or functions, whenever this abstraction is worthwhile. One should also work out the things which are proved in § 7 and accept certain basic principles of linear functional analysis quoted there for easier references, until they are applied in later chapters. In other words, even the 'completely linear' sections which we have included for your convenience serve only as a vehicle for progress in nonlinearity. Another point that makes the text introductory is the use of an essentially uniform mathematical language and way of thinking, one which is no doubt familiar from elementary lectures in analysis that did not worry much about its connections with algebra and topology. Of course we shall use some elementary topological concepts, which may be new, but in fact only a few remarks here and there pertain to algebraic or differential topological concepts and methods.

Keywords

banach spaces compactness differential equation functional analysis Hilbert space maximum spectral theory topological vector space

Authors and affiliations

  • Klaus Deimling
    • 1
  1. 1.Gesamthochschule PaderbornPaderbornFederal Republic of Germany

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-662-00547-7
  • Copyright Information Springer-Verlag Berlin Heidelberg 1985
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-662-00549-1
  • Online ISBN 978-3-662-00547-7
  • About this book