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Differential Equations with Involutions

  • Alberto Cabada
  • F. Adrián F. Tojo
Book

Part of the Atlantis Briefs in Differential Equations book series (ABDE)

Table of contents

  1. Front Matter
    Pages i-xiv
  2. Involutions

    1. Front Matter
      Pages 1-1
    2. Alberto Cabada, F. Adrián F. Tojo
      Pages 3-16
    3. Alberto Cabada, F. Adrián F. Tojo
      Pages 17-23
  3. Green’s Functions

    1. Front Matter
      Pages 25-25
    2. Alberto Cabada, F. Adrián F. Tojo
      Pages 27-73
    3. Alberto Cabada, F. Adrián F. Tojo
      Pages 75-99
    4. Alberto Cabada, F. Adrián F. Tojo
      Pages 101-122
  4. Applications

    1. Front Matter
      Pages 123-123
    2. Alberto Cabada, F. Adrián F. Tojo
      Pages 125-151
  5. Back Matter
    Pages 153-154

About this book

Introduction

This monograph covers the existing results regarding Green’s functions for differential equations with involutions (DEI).The first part of the book is devoted to the study of the most useful aspects of involutions from an analytical point of view and the associated algebras of differential operators. The work combines the state of the art regarding the existence and uniqueness results for DEI and new theorems describing how to obtain Green’s functions, proving that the theory can be extended to operators (not necessarily involutions) of a similar nature, such as the Hilbert transform or projections, due to their analogous algebraic properties. Obtaining a Green’s function for these operators leads to new results on the qualitative properties of the solutions, in particular maximum and antimaximum principles.

Keywords

Differential Equations with reflection Functional-Differential Equations of Carleman type Green's functions Maximum principles Ordinary Differential Equations with involutions

Authors and affiliations

  • Alberto Cabada
    • 1
  • F. Adrián F. Tojo
    • 2
  1. 1.Departamento de Análise MatemáticaUniversidade de Santiago de Compostela Departamento de Análise MatemáticaSantiago de CompostelaSpain
  2. 2.Departamento de Análise MatemáticaUniversidade de Santiago de Compostela Departamento de Análise MatemáticaSantiago de CompostelaSpain

Bibliographic information

  • DOI https://doi.org/10.2991/978-94-6239-121-5
  • Copyright Information Atlantis Press and the author(s) 2015
  • Publisher Name Atlantis Press, Paris
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-94-6239-120-8
  • Online ISBN 978-94-6239-121-5
  • Series Print ISSN 2405-6405
  • Series Online ISSN 2405-6413
  • Buy this book on publisher's site