Oscillation Theory of Delay Differential Equations

ISBN-13: 9780198535829 / Angielski / Twarda / 1991 / 380 str.

I. Györi; G. Ladas

Opis

In recent years there has been a resurgence of interest in the study of delay differential equations motivated largely by new applications in physics, biology, ecology, and physiology. The aim of this monograph is to present a reasonably self-contained account of the advances in the oscillation theory of this class of equations. Throughout, the main topics of study are motivated by applications as diverse as the populations of blowflies, logistic equations in ecology, the survival of red blood cells in animals, integro-differential equations, and the motion of the tips of growing plants.The authors begin by reviewing the basic theory of delay differential equations including the fundamental results of existence and uniqueness of solutions and the theory of the Laplace and z-transforms. Consequently, little prior knowledge of the subject is required other than a firm grounding in the main techniques of differential equation theory. As a result this book provides an invaluable reference to the recent work both for mathematicians and for all those whose reseach includes the study of this fascinating class of differential equations.

In recent years there has been a resurgence of interest in the study of delay differential equations motivated largely by new applications in physics, biology, ecology, and physiology. The aim of this monograph is to present a reasonably self-contained account of the advances in the oscillation theory of this class of equations. Throughout, the main topics of study are motivated by applications as diverse as the populations of blowflies, logistic equations in ecology, the survival of red blood cells in animals, integro-differential equations, and the motion of the tips of growing plants.

Recenzje

This very good monograph contains some of the most recent important developments in the oscillation theory of differential equations with deviating arguments. ... The book is well written ... and reads well. ... This book is self-contained and provides an excellent reference to the recent work for research workers in this interesting field.

Spis treści

Preface; Introduction; Acknowledgements; Preliminaries; Oscillations of linear scalar delay equations; Generalized characteristic equation and existence of positive solutions; Linearized oscillation theory and applications to mathematical biology; Oscillations of systems of delay equations; Oscillations of neutral differential equations; Oscillations of delay difference equations; Oscillations of equations with piecewise constant arguments; Oscillations of integro-differential equations; Oscillations of second- and higher-order equations; Applications of oscillation theory to the asymptotic behaviour of solutions; Miscellaneous topics; Bibliography.