الفهرس 
Chapter 1 IntroductionOnly 14 pages are availabe for public view
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Abstract
”Dissertation Abstract Actually, In recent years there has been an evident research activity regarding the oscillation of solutions of DDEs. This is due to the realization of the great importance that DEs equations have in various applications, where new applications that include DDEs continue to appear with increasing frequency in modeling various phenomena in biology, ecology, physiology, physics and others. Therefore, finding solutions to DEs or deducing important properties of these solutions has attracted the attention of many authors and researchers. In fact, there are many results related to studying the oscillation of equations of the first and second orders, while we find that it is much less for DEs of the third and higher orders, so the main objective of this thesis is to shed light on many equations of the second, third and higher orders, through the study of asymptotic behavior to solutions of these equations in different ways and compare the results. The main objective of this thesis is to contribute to the great development of oscillation theory for second and higher order DDEs. Our results in this thesis improve some previous results (as shown in the examples and notes found throughout the chapters of the thesis). We discuss in detail asymptotic behavior and oscillatory of some classes of nonlinear DEs of second, third, and higher (odd) order as the following: In Chapter 1, we covered some fundamental definitions and elementary results that related to the subject of study in this thesis. In Chapter 2, we established some new oscillation results based on comparison technique and generalized Riccati substitution for two class of second-order DE. In Chapter 3, we obtained sufficient conditions that guarantee the oscillation for all solutions of class of third-order DDE by using different methods in both cases canonical and noncanonical. In Chapter 4, we studied oscillatory behaviour and asymptotic properties of the solutions for class of third-order NDDE of mixed type. In Chapter 5, we discussed oscillation behavior of solutions of class third-order damped NDDE. Also, in Chapter 6, we postulated new sufficient conditions that ensure all solutions of class of higher-order NDD are oscillatory or almost oscillatory. Most of our results have been published in peer-reviewed journals. Keywords: Oscillation, Differential Equations, higher order.