Oscillation Theory For Second Order Dynamic Equations

Volume 5

Ravi P. Agarwal, Said R. Grace, Donal O'Reagan

412 pages, parution le 04/12/2002

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Résumé

This book considers a rapidly developing area of research known as the qualitative theory of dynamics equations. In fact, in the last 50 years the oscillation theory of ordinary, functional, neutral, partial, and impulsive differential equations, and their discrete versions has attracted many researchers resulting in a large volume of literature. There are many books that deal exclusively with the oscillation of solutions of differential equations but most of these appeal only to researchers already familiar with the subject. Thus, in an effort to bring the subject to a new and wider audience, this book presents a compact but thorough guide to oscillation theory for second order differential equations with deviating arguments, neutral functional differential equations, and impulsive differential equations. Conjugacy criteria for second order ordinary differential equations are also provided. There are also numerous examples throughout the text which not only illustrate the theory, but also provide motivation for new directions.

Contents

Chapter 1 Preliminaries

Introduction
Initial Value Problem, Oscillation and Nonoscillation
Continuability and Boundedness
Some Basic Results for Second Order Linear Ordinary Differential Equations
Some Useful Criteria for First Order Functional Differential Equations
Some Useful Results from Analysis and Fixed Point Theorems
Notes and General Discussions
References

Chapter 2 Oscillation of Differential Equations with Deviating Arguments

Introduction
Oscillation Theorems (I)
Oscillation Theorems (II)
Comparison Theorems for Second Order Functional Differential Equations
Oscillation of Functional Equations with a Damping Term
Oscillation of Second Order Linear Delay Differential Equations
Oscillation of Forced Functional Differential Equations
Oscillation of Functional Equations with Damping and Forcing Terms
Necessary and Sufficient Conditions for the Oscillation of Forced Equations
Oscillation for Perturbed Differential Equations
Asymptotic Behavior of Oscillatory Solutions of Functional Equations
Notes and General Discussions
References

Chapter 3 Oscillation of Neutral Functional Differential Equations

Introduction
Oscillation of Nonlinear Neutral Equations
Oscillation of Neutral Equations with Damping
Oscillation of Forced Neutral Equations
Oscillation of Neutral Equations of Mixed Type
Necessary and Sufficient Conditions for Oscillations of Neutral Equations with Deviating Arguments
Comparison and Linearized Oscillation Theorems for Neutral Equations
Existence of Nonoscillatory Solutions of Neutral Delay Differential Equations
Asymptotic Behavior of Nonoscillatory Solutions of Neutral Nonlinear Delay Differential Equations
Notes and General Discussions
References

Chapter 4 Conjugacy and Nonoscillation for Second Order Differential Equations

Introduction
Conjugacy of Linear Second Order Ordinary Differential Equations
Nonoscillation Theorems
Integral Conditions and Nonoscillation
Notes and General Discussions
References

Chapter 5 Oscillation of Impulsive Differential Equations

Introduction
Oscillation Criteria for Impulsive Delay Differential Equations
Oscillation of Second Order Linear Differential Equations with Impulses
Oscillation of Second Order Nonlinear Differential Equations with Impulses
Notes and General Discussions
References

Caractéristiques techniques

	PAPIER
Éditeur(s)	Taylor and Francis Books
Auteur(s)	Ravi P. Agarwal, Said R. Grace, Donal O'Reagan
Parution	04/12/2002
Nb. de pages	412
Format	17,8 x 25,2
Couverture	Relié
Poids	856g
Intérieur	Noir et Blanc
EAN13	9780415300742
ISBN13	978-0-415-30074-2