Overview
- New approach which helps the reader to decide about solvability of various boundary value problems with state-dependent impulses
- Contains recent and unique existence results for state-dependent impulsive problems with general linear boundary conditions
- Includes existence theorems for singular impulsive problems
- Shows how to generalize presented existence results
- Includes supplementary material: sn.pub/extras
Part of the book series: Atlantis Briefs in Differential Equations (ABDE, volume 6)
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Table of contents (10 chapters)
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Front Matter
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Problems with Impulses at Fixed Times
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Front Matter
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Problems with State-Dependent Impulses
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Front Matter
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Back Matter
Keywords
About this book
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.
Authors and Affiliations
Bibliographic Information
Book Title: State-Dependent Impulses
Book Subtitle: Boundary Value Problems on Compact Interval
Authors: Irena Rachůnková, Jan Tomeček
Series Title: Atlantis Briefs in Differential Equations
DOI: https://doi.org/10.2991/978-94-6239-127-7
Publisher: Atlantis Press Paris
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature B.V. 2015
Softcover ISBN: 978-94-6239-126-0Published: 09 October 2015
eBook ISBN: 978-94-6239-127-7Published: 29 September 2015
Series ISSN: 2405-6405
Series E-ISSN: 2405-6413
Edition Number: 1
Number of Pages: XV, 190
Number of Illustrations: 7 b/w illustrations
Topics: Ordinary Differential Equations