الفهرس 
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Abstract
The aim of this thesis is to study the sufficient conditions for the oscillation of all solutions of linear delay differential equations and nonlinear delay differential equations where in recent years there has been much research activity concerning the oscillation of solutions of delay differential equations. New applications, which involve delay differential equations, continue to arise with increasing frequency in the modeling of diverse phenomena in physics, biology, ecology and physiology. In this thesis we will discuss the oscillation behavior of the solutions of the delay differential equations with positive coefficients and with several positive and negative coefficients and we will discuss the oscillatory behavior of the solutions of the nonlinear delay differential equations. We have to mention here that each chapter contains its background material, where we list the most important relevant results that can be found in the literature. In most cases we will give some examples to illustrate the results obtained by us and others The investigation of the oscillation of delay differential equation may be done in many directions. Among these an oftenconsidered way is to determine the properties of roots of the characteristic equation. In another way to prove some of these many authors using the exposit conditions involving the coefficients and delays in order to obtain sufficient conditions for oscillations. ?Generally, It is not possible to obtain analytic solutions to linear and nonlinear delay differential equations. So many authors tends to the qualitative study for them, which are concerned with how to deduce important characteristic of the solutions of delay differential equations without solving them.