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State-Dependent Impulses

Boundary Value Problems on Compact Interval

  • Irena Rachůnková
  • Jan Tomeček
Book

Part of the Atlantis Briefs in Differential Equations book series (ABDE, volume 6)

Table of contents

  1. Front Matter
    Pages i-xv
  2. Irena Rachůnková, Jan Tomeček
    Pages 1-17
  3. Problems with Impulses at Fixed Times

    1. Front Matter
      Pages 19-19
    2. Irena Rachůnková, Jan Tomeček
      Pages 21-39
    3. Irena Rachůnková, Jan Tomeček
      Pages 41-62
    4. Irena Rachůnková, Jan Tomeček
      Pages 63-87
  4. Problems with State-Dependent Impulses

    1. Front Matter
      Pages 111-111
    2. Irena Rachůnková, Jan Tomeček
      Pages 113-125
    3. Irena Rachůnková, Jan Tomeček
      Pages 127-142
    4. Irena Rachůnková, Jan Tomeček
      Pages 143-155
    5. Irena Rachůnková, Jan Tomeček
      Pages 157-169
    6. Irena Rachůnková, Jan Tomeček
      Pages 171-187
  5. Back Matter
    Pages 189-190

About this book

Introduction

This book offers the reader a new approach to the solvability of boundary value problems with state-dependent impulses and provides recently obtained existence results for state dependent impulsive problems with general linear boundary conditions. It covers fixed-time impulsive boundary value problems both regular and singular and deals with higher order differential equations or with systems that are subject to general linear boundary conditions. We treat state-dependent impulsive boundary value problems, including a new approach giving effective conditions for the solvability of the Dirichlet problem with one state-dependent impulse condition and we show that the depicted approach can be extended to problems with a finite number of state-dependent impulses. We investigate the Sturm–Liouville boundary value problem for a more general right-hand side of a differential equation. Finally, we offer generalizations to higher order differential equations or differential systems subject to general linear boundary conditions.

Keywords

Fixed Point Approach General Linear Boundary Conditions Impulses at Fixed Times Impulsive Boundary Value Problems State-dependent Impulses

Authors and affiliations

  • Irena Rachůnková
    • 1
  • Jan Tomeček
    • 2
  1. 1.Faculty of SciencePalacký UniversityOlomoucCzech Republic
  2. 2.Faculty of SciencePalacký UniversityOlomoucCzech Republic

Bibliographic information

  • DOI https://doi.org/10.2991/978-94-6239-127-7
  • Copyright Information Atlantis Press and the author(s) 2015
  • Publisher Name Atlantis Press, Paris
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-94-6239-126-0
  • Online ISBN 978-94-6239-127-7
  • Series Print ISSN 2405-6405
  • Series Online ISSN 2405-6413
  • Buy this book on publisher's site