Oscillation theory for neutral differential equations with delay

書誌事項

Oscillation theory for neutral differential equations with delay

D.D. Bainov, D.P. Mishev

A. Hilger, c1991

大学図書館所蔵 件 / 25

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注記

Bibliographical references: p. [268]-277

Includes index

内容説明・目次

内容説明

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.

目次

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

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