Impulsive differential inclusions : a fixed point approach / by John R. Graef, Johnny Henderson, Abdelghani Ouahab.

Format:

Book

Author/Creator:

Graef, John R., 1942-

Contributor:

Henderson, Johnny.

Ouahab, Abdelghani.

Series:

De Gruyter Series in Nonlinear Analysis and Applications

De Gruyter Series in Nonlinear Analysis and Applications ; 20

Language:

English

Subjects (All):

Boundary value problems.

Differential equations.

Prediction theory.

Stochastic processes.

Physical Description:

1 online resource (412 p.)

Edition:

1st ed.

Place of Publication:

Berlin ; Boston : Walter de Gruyter GmbH & Co., KG, [2013]

Language Note:

English

Summary:

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.

Contents:

Front matter

Contents

Notations

Chapter 1. Introduction and Motivations

Chapter 2. Preliminaries

Chapter 3. FDEs with Infinite Delay

Chapter 4. Boundary Value Problems on Infinite Intervals

Chapter 5. Differential Inclusions

Chapter 6. Differential Inclusions with Infinite Delay

Chapter 7. Impulsive FDEs with Variable Times

Chapter 8. Neutral Differential Inclusions

Chapter 9. Topology and Geometry of Solution Sets

Chapter 10. Impulsive Semilinear Differential Inclusions

Chapter 11. Selected Topics

Appendix

Bibliography

Index

Notes:

Description based upon print version of record.

Description based on online resource; title from PDF title page (ebrary, viewed November 22, 2013).

ISBN:

9783110295313

3110295318

OCLC:

858762153