Oscillation theory of differential equations with deviating arguments

320 Pages·1987·29.94 MB·English

by  G. S. Ladde

Oscillation Theory of
Differential Equations with
Deviating Arguments
PURE AND APPLIED MATHEMATICS
A Program of MOllOgraphs, Textbooks, alld Leclllre Notes
EXECUTIVE EDITORS
Earl J. Taft Zuhaif Nashed
Rutgers University University of Dd;n• .' Ore
New Brunswick. Ne!N Jersey Ne'WOrk. Deio ...., ore
CHAIRMEN OF THE EDITORIAL BOARD
S. Kobayashi Edwin liewitt
University of Colifornia, Berkeley U"II'ers;ty 01 Washington
Berkeley, California Seoule, Washington
EDITORIAL BOARD
M. S. Baouendi Donald Possman
Purdue University University Of Wisconsin-Madison
Jack K. Hale Fred S. Roberts
Brown University Rutgers University
Marvin Marcus Cion-Carlo Rota
University 0/ California. Sanla Barbara Mossochuseas Institute 01
TechnoloKY
IV. S. Massey
Yale University David Russell
Unil)erslty of Wisconsin-Madison
Leopolda Nachbin
Centro BTasi/eiro de Pesquisas Fisicos Jane Cronin Scanlo"
and University of Rochester Rutgers UniverSIty
Anil Nerode Walter Schempp
Cornell University Universita( Siegen
Mark Teply
University of Wisconsin·Milwaukee
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5. L. Nar/ci, E. Beckens/ein. and C. Bachman, Functional Analysis and
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7. L. Dornhoff. Group Representation Theory (in two parts). Part A;
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17. C. Procesl. Rings with Polynomi<tl Identities (1973)
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Theory of Differcntial Equations with Dcvlating Arguments (1987)
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111. T. Okubo. Differential Geometry (1987)
Other Volumes itl Preparation
Oscillation Theory of
Differential Equations with
Deviating Arguments
G. S. LADDE
V. LAKSHMlKANTHAM
The University oJ Texas
Arlington. Texas
B.G. ZHANG
Shandong College of Oceanography
Qlngdaa. Shandong
People~ RepublIC of China
MARCEL DEKKER, INC. New York and Basel
Library of Congress Cataloging In Publication Data
Ladde, G. S.
Oscillation theory of differential equations with
deviating arguments.
(Pure and applied mathematics; 110)
Bibliography: p.
Inciudes Index.
1. Differential equations. 2. Oscillations.
I. Lakshmikantham, V. U. Zhang, B. G., (date).
ill. Title. IV. Series: Monographs and textbooks in pure
and applied mathematics; v. 110.
QA372. L19 1987 515.3'5 87-9232
ISBN 0-8247-7738-7"
265885
COPYRIGHT C 1987 by MARCEL DEKKER, rNC. ALL RIGHTS RESERVED
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Preface
The mathematical modellng of several real-world problems leads to
differential equations that depend on the past history rather than only the
current state. The models may have discrete time lags as well as distrib
uted lags or delays.
Most of the work in the theory of oscillations is centered around second
or hlgher order ordinary differential equations (ODE) because of the fact
that the first order scalar OOEs do not possess oscillatory behavior.
Bernoulli (1728) studied the problem of sound vlbratlng In a tube of flnlte
length and investigated the properties of first order ordinary differential
equations with deviating arguments (ODEWDA). Myskis investigated several
oscUlation problems of first order ODEWDA, which are recorded in his
book. Since 1950 oscillation theory of ODEWDA has received the attention
of several applied mathematicians as well as other scientists around the
world. In light of this. it is essential to present an up-to-date account in
a systematic way.
This book offers a systematic treatment of oscUlation and nonoscillattOD
theory of differential equations with deviatlng arguments. The book Is
divided into six chapters. The first chapter conSists of preUminary material
that is essential for the rest of the book. Chapters 2 and 3 deal with first
order linear and nonlinear differential equations with deviating arguments.
Chapter 4 is devoted to second order equations. Chapter 5 extends the study
to higher order equations. In Chapter 6, we introduce the oscillation theory
to systems of differential equaUons with deviating arguments.
Some important features of the book are the following:
(I) This Is the first English language book tbat offers a systematic study
of the theory of oscUlation of ordinary differential equations with devi
ating arguments. It complements the book by Swanson [260] which dis
cusses the oscillation theory of linear ordinary differential equations
only.
(it) This book stresses the importance of deviattng arguments in the sense
that their presence causes or destroys the oscillation phenomena,
III
Iv Preface
and does Dot merely preserve the oscUla tory behavtor of equations
without deviating arguments.
(ill) This book contains recent results and consoquently is a valuable source
for research workers In the field.
We wish to express our thanks to Ms. Vickie Kearn and the staff
of Marcel Dekker, Inc., for their cooperation during the publlcatlon of the
book. We also wish to thank Mrs. Sandra Weber for her excellent typtog of
the manuscript.
o. S. Ladde
V. Lakshmlkantham
B. O. Zhang