Qualitative investigations and approximate methods for impulsive equations / Snezhana G. Hristova.

Format:

Book

Author/Creator:

Hristova, Snezhana G.

Language:

English

Subjects (All):

Impulsive differential equations.

Physical Description:

1 online resource (179 p.)

Edition:

1st ed.

Place of Publication:

New York : Nova Science Publishers, Inc., c2009.

Language Note:

English

Summary:

This new and important book expands the idea of the wide specter of the theory of impulsive equations to the theoretical and applied researchers in mathematics and provides them a tool and motivation for deeper investigations and applications of these equations to real world problems. It deals with the theory of impulsive differential equations, which is a relatively new area and seems to hold a considerable potential. This field started gaining interest around 1980 and today we have several hundred researches working in it and a couple of thousand publications.Many of the theorectical results obtained in the field of impulsive differential equations have already been used in the process of modeling and investigating the properties of real life processes in the sciences and technologies.

Contents:

Intro

QUALITATIVEINVESTIGATIONSANDAPPROXIMATEMETHODSFORIMPULSIVEEQUATIONS

Contents

Preface

Introduction

A.ImpulsiveDifferentialEquations

B.ImpulsiveDifferential-DifferenceEquations

C.ImpulsiveHybridEquations

D.ImpulsiveDifferentialEquationswith"Supremum"

Chapter1MethodoftheIntegralInequalitiesforQualitativeInvestigationsofImpulsiveEquations

1.1.LinearImpulsiveIntegralInequalities

1.2.NonlinearImpulsiveIntegralInequalities

1.3.ImpulsiveIntegralInequalitiesforPiecewiseContinuousFunctionswithaDelayoftheArgument

1.4.ImpulsiveIntegralInequalitiesforScalarPiecewiseCon-tinuousFunctionsofTwoVariables

1.5.ApplicationsoftheImpulsiveIntegralInequalities

Chapter2Lyapunov'sMethodforBoundednessandPeriodicityoftheSolutionsofImpulsiveEquations

2.1.PiecewiseContinuousLyapunovFunctions

2.2.BoundednessoftheSolutionsofImpulsiveDifferentialEquations

2.3.BoundednessoftheSolutionsofImpulsiveEquationswith"Supremum"

2.4.BoundednessoftheSolutionsofImpulsiveHybridEquations

2.5.LyapunovFunctionsandPeriodicSolutionsofImpulsiveDifferentialEquations

Chapter3Monotone-IterativeTechniquesforImpulsiveEquations

3.1.Monotone-IterativeTechniquesforTheinitialValueProblemforImpulsiveDifferential-DifferenceEquationswithVariableMomentsofImpulses

3.2.Monotone-IterativeTechniquesfortheInitialValueProblemforSystemsofImpulsiveFunctional-DifferentialEquations

3.3.Monotone-IterativeTechniquesforPeriodicBoundaryValueProblemforSystemsofImpulsiveDifferential-DifferenceEquations

Chapter4MethodofQuasilinearizationforImpulsiveDifferentialEquations

4.1.MethodofQuasilinearizationfortheInitialValueProblemforSystemsofImpulsiveDifferentialEquations

4.2.MethodofQuasilinearizationforaLinearBoundaryValueProblemforScalarImpulsiveDifferentialEquations.

4.3.MethodofQuasilinearizationforPeriodicBoundaryValueProblemforSystemsofImpulsiveDifferentialEquations

References

Index

Blank Page.

Notes:

Description based upon print version of record.

Includes bibliographical references (p. [157]-165) and index.

Description based on print version record.

ISBN:

1-61470-722-7

OCLC:

756675541