Impulsive Differential Inclusions: A Fixed Point Approach

John R. Graef; Johnny Henderson; Abdelghani Ouahab

Published by De Gruyter 2013

Impulsive Differential Inclusions

A Fixed Point Approach

John R. Graef , Johnny Henderson and Abdelghani Ouahab

Volume 20 in the series De Gruyter Series in Nonlinear Analysis and Applications

https://doi.org/10.1515/9783110295313

Overview
Contents

About this book

Differential equations with impulses arise as models of many evolving processes that are subject to abrupt changes, such as shocks, harvesting, and natural disasters. These phenomena involve short-term perturbations from continuous and smooth dynamics, whose duration is negligible in comparison with the duration of an entire evolution. In models involving such perturbations, it is natural to assume these perturbations act instantaneously or in the form of impulses. As a consequence, impulsive differential equations have been developed in modeling impulsive problems in physics, population dynamics, ecology, biotechnology, industrial robotics, pharmacokinetics, optimal control, and so forth. There are also many different studies in biology and medicine for which impulsive differential equations provide good models.

During the last 10 years, the authors have been responsible for extensive contributions to the literature on impulsive differential inclusions via fixed point methods. This book is motivated by that research as the authors endeavor to bring under one cover much of those results along with results by other researchers either affecting or affected by the authors' work. The questions of existence and stability of solutions for different classes of initial value problems for impulsive differential equations and inclusions with fixed and variable moments are considered in detail. Attention is also given to boundary value problems. In addition, since differential equations can be viewed as special cases of differential inclusions, significant attention is also given to relative questions concerning differential equations. This monograph addresses a variety of side issues that arise from its simpler beginnings as well.

Author / Editor information

John R. Graef, University of Tennessee at Chattanooga, Tennessee, USA; Johnny Henderson, Baylor University, Waco, Texas, USA; Abdelghani Ouahab, University of Sidi Bel Abbes, Sidi Bel Abbes, Algeria.

Supplementary Materials

Contents

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Frontmatter Publicly Available Download PDF	i
Contents Publicly Available Download PDF	vii
Notations Requires Authentication Unlicensed Licensed Download PDF	xi
Chapter 1. Introduction and Motivations Requires Authentication Unlicensed Licensed Download PDF	1
Chapter 2. Preliminaries Requires Authentication Unlicensed Licensed Download PDF	11
Chapter 3. FDEs with Infinite Delay Requires Authentication Unlicensed Licensed Download PDF	47
Chapter 4. Boundary Value Problems on Infinite Intervals Requires Authentication Unlicensed Licensed Download PDF	86
Chapter 5. Differential Inclusions Requires Authentication Unlicensed Licensed Download PDF	98
Chapter 6. Differential Inclusions with Infinite Delay Requires Authentication Unlicensed Licensed Download PDF	140
Chapter 7. Impulsive FDEs with Variable Times Requires Authentication Unlicensed Licensed Download PDF	154
Chapter 8. Neutral Differential Inclusions Requires Authentication Unlicensed Licensed Download PDF	171
Chapter 9. Topology and Geometry of Solution Sets Requires Authentication Unlicensed Licensed Download PDF	199
Chapter 10. Impulsive Semilinear Differential Inclusions Requires Authentication Unlicensed Licensed Download PDF	254
Chapter 11. Selected Topics Requires Authentication Unlicensed Licensed Download PDF	306
Appendix Requires Authentication Unlicensed Licensed Download PDF	357
Bibliography Requires Authentication Unlicensed Licensed Download PDF	369
Index Requires Authentication Unlicensed Licensed Download PDF	399

(Deutsch)

Language: English
Publisher: De Gruyter
Audience: Researchers, Graduate and PhD Students in Mathematics, Academic Libraries
Pages
- Front matter: 10
- Main content: 400
Keywords: Impulsive Functional Differential Equation; Boundary Value Problem; Stability; Infinite Delay; Contraction; Differential Inclusion; Hyperbolic Differential Inclusion; Variable Times; Condensing; Controllability; Stochastic Differential Equation; Filippov's Theorem; Relaxation; Seeping Process; Normal Cone; Viable Solution

eBook

Published: July 31, 2013
ISBN: 9783110295313

Hardcover

Published: July 17, 2013
ISBN: 9783110293616