1st Edition

Oscillation Theory for Neutral Differential Equations with Delay

By D.D Bainov, D.P Mishev Copyright 1991
    288 Pages
    by CRC Press

    With neutral differential equations, any lack of smoothness in initial conditions is not damped and so they have proven to be difficult to solve. Until now, there has been little information to help with this problem.

    Oscillation Theory for Neutral Differential Equations with Delay fills a vacuum in qualitative theory of functional differential equations of neutral type. With much of the presented material previously unavailable outside Eastern Europe, this authoritative book provides a stimulus to research the oscillatory and asymptotic properties of these equations. It examines equations of first, second, and higher orders as well as the asymptotic behavior for tending toward infinity. These results are then generalized for partial differential equations of neutral type. The book also describes the historical development of the field and discusses applications in mathematical models of processes and phenomena in physics, electrical control and engineering, physical chemistry, and mathematical biology.

    This book is an important tool not only for mathematicians, but also for specialists in many fields including physicists, engineers, and biologists. It may be used as a graduate-level textbook or as a reference book for a wide range of subjects, from radiophysics to electrical and control engineering to biological science.

    PREFACE
    NOTATION

    INTRODUCTION
    Preliminary notes
    Auxiliary assertions

    FIRST ORDER NEUTRAL ORDINARY DIFFERENTIAL EQUATIONS
    First order linear differential equations
    First order differential equations with constant coefficients
    First order differential equations with distributed delay
    First order nonlinear differential equations
    Oscillation and comparison of results in neutral differential equations and their applications to the delay logistic equation
    Notes and comments to chapter 2

    SECOND ORDER NEUTRAL ORDINARY DIFFERENTIAL EQUATIONS
    Second order linear differential equations
    Second order differential equations with constant coefficients
    Second order differential equations with distributed delay
    Second order nonlinear differential equations
    Distribution of the zeros of the solutions of neutral differential equations
    Notes and comments to chapter 3

    NTH ORDER NEUTRAL ORDINARY DIFFERENTIAL EQUATIONS
    nth order linear differential equations
    nth order differential equations with constant coefficients
    nth order nonlinear differential equations
    Notes and comments to chapter 4

    SYSTEMS OF ORDINARY DIFFERENTIAL EQUATIONS OF NEUTRAL TYPE
    Linear systems of ordinary differential equations with constant coefficients
    Notes and comments to chapter 5

    NEUTRAL PARTIAL DIFFERENTIAL EQUATIONS
    Linear parabolic differential equations
    Nonlinear parabolic differential equations
    Parabolic differential equations with "maxima"
    Linear hyperbolic differential equations
    Nonlinear hyperbolic differential equations
    Hyperbolic differential equations with "maxima"
    Notes and comments to chapter 6

    REFERENCES
    INDEX

    Biography

    D.D Bainov, D.P Mishev