الفهرس 
Chapter 1 IntroductionOnly 14 pages are availabe for public view
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Abstract
Differential equations (DEs) are crucial for understanding real-life problems and phenomena, or at the very least for knowing the characteristics of the solutions to the equations resulting from modeling these phenomena. However, DEs like the ones presented that are utilized to address real-world issues may not be explicitly solvable, i.e., may not have closed-form solutions. Only equations with simple forms accept the solutions supplied by explicit formulae. In recent decades, different models of DEs have been established in various fields, leading to stimulating the research in the qualitative theory of DEs. Neutral differential equations (NDEs) are a type of functional differential equation in which the highest derivative of the unknown function appears with and without delay. The qualitative analysis of such equations has a lot of practical use in addition to its theoretical value. This is due to the fact that NDEs appear in a variety of situations, such as problems involving lossless transmission lines in electric networks (as in high-speed computers where such lines are used to interconnect switching circuits), the study of vibrating masses attached to an elastic bar, and the solution of variational problems with time delays. The essence of oscillation theory is to establish conditions for the existence of oscillatory (non-oscillatory) solutions, to study the laws of distribution of the zeros, to obtain estimates of the distance between the neighboring zeros and the number of zeros in a given interval, to describe the relationship between the oscillatory and other basic properties of the solutions of various classes of DEs. The oscillation theory has become a significant numerical mathematical tool for many disciplines and high technologies. The main objective of this thesis is to discuss and study the oscillatory behavior of solutions of DEs of higher order. The most important results obtained can be summarized as follows : - The development made in the study of the oscillatory behavior of solutions to second-order equations has been extended to higher-order equations. - By obtaining new or improved relationships between the solution and its various derivatives or between the solution with and without delay, we were able to create new oscillation criteria that give better results in testing the oscillation of higher-order equations. Obtaining criteria of an iterative nature contributes greatly to the development and improvement of oscillation criteria, as it helps to apply criteria more than once while the relevant results fail.