Ladde G.S., Lakshmikantham V., Zhang B.G. Oscillation theory of differential equations with deviating arguments

Marcel Dekker, 1987. — 320 p.
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 distributed 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 ODEs do not possess oscillatory behavior. Bernoulli (1728) studied the problem of sound vlbratlng In a tube of finite length and investigated the properties of first order ordinary differential equations with deviating arguments (ODEWDA). Myskis investigated several oscillation 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 oscillation and nonoscillation theory of differential equations with deviatlng arguments. The book is
divided into six chapters. The first chapter consists of preliminary 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 equations with deviating arguments.