الفهرس 
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Abstract
This thesis discussed, in detail, the oscillation and the asymptotic behavior of solutions of the class of second and even-order nonlinear DDEs. Specifically, the topics dealt with include the following: Finding conditions for oscillation of all solution. Finding conditions that ensure that the solutions of the equation are either oscillatory or converges to zero. Finding conditions for the nonexistence of so-called Kneser solutions. Moreover, we will use some main techniques for finding the oscillation criteria, including the following: (i) Riccati transformation technique. (ii) New comparison principles enable us to deduce properties of the even-order nonlinear DE from the oscillation of a first-order nonlinear DDE and some other methods. This thesis contains several remarks and illustrative examples as applications of our results. The thesis consists of six chapters. Chapter 1 : This chapter is introductory and it deals with the problem of oscillation of second/even-order DEs. It contains some basic definitions and elementary results that will be used throughout the next chapters. Chapter 2: By establishing a new relationship between the solution x and the corresponding function z, we obtain new oscillation criteria for the second-order NDDE, which improves the previous results in the literature. Further, we get new oscillation conditions for the second-order DDE with a sublinear neutral term. Chapter 3: This chapter aims to study the oscillatory behavior for second-order NDEs with a damping term. We consider the noncanonical case which always leads to two independent conditions for oscillation. We are working to improve related results by simplifying the conditions, based on taking a different approach that leads to one condition. Moreover, we obtain different forms of conditions to expand the application area. Chapter 4: We study the oscillatory behavior of solutions of the second-order DE with a mixed neutral term under the noncanonical case. We follow a new approach based on deducing a new relationship between the solution and the corresponding function. Using this new relationship, we first obtain one condition that ensures the oscillation. Moreover, by introducing a generalized Riccati substitution, we get a new criterion for oscillation. Chapter 5: In this chapter, we consider the even-order NDDE with several delays. By using both the Riccati substitution technique and comparison with delay equations of first-order, we establish new oscillation criteria in non-canonical case. Our new criteria are simplifying and complementing some related results that have been published in the literature. Chapter 6: In this chapter, we introduce the conclusion and future works.