الفهرس 
Chapter 1Only 14 pages are availabe for public view
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Abstract
In recent years, there has been a notable increase in research activity focused on understanding the oscillatory behavior of solutions in delay differential equations (DDEs) and neutral differential equations (NDEs). The growing recognition of the pivotal role these equations play in diverse applications, such as biology, ecology, physiology, and physics, has spurred continuous exploration. With new applications emerging, the significance of finding solutions and uncovering essential properties of these solutions has captured the attention of numerous authors and researchers. While there exists a wealth of results concerning the oscillation of first and second-order equations, there is a comparatively limited body of work on differential equations (DEs) of the higher orders. Consequently, the primary objective of this thesis is to illuminate equations of the higher orders. The focus lies in studying the asymptotic behavior of solutions through various approaches and conducting comparative analyses of the results. The overarching aim is to contribute to the substantial development of oscillation theory for higher-order DDEs and NDEs. The findings presented in this thesis not only address existing gaps but also enhance and refine certain aspects of prior results, as demonstrated in the examples and notes scattered throughout the chapters. The main objective of this thesis is to discuss and study the oscillatory behavior of solutions of DEs of higher order. The thesis is divided into six chapters. The thesis comprises six chapters, each addressing distinct aspects of functional differential equations. Chapter 1 serves as an introduction, providing foundational definitions, results, and theorems crucial for subsequent discussions. In Chapter 2, we investigate the asymptotic and oscillatory properties of a distinctive class of third-order linear differential equations characterized by multiple delays in a noncanonical case. Employing the comparative method and the Ric- cati method, we introduce novel and rigorous criteria to discern whether the solutions of the examined equation exhibit oscillatory behavior or tend toward zero. In Chapter 3, the focus is on investigating the asymptotic behavior of non-oscillatory solutions in a specific class of third-order neutral differential equations, utilizing Riccati substitution and the Philos function class. Novel criteria of the Kamenev type are developed, ensuring the convergence of all non-oscillatory solutions to zero. Chapter 4 explores the qualitative behavior of solutions in a particular class of fourth-order half-linear neutral differential equations, aiming to enhance the relationship between the solution and its corresponding function. A new criterion is proposed for determining oscillatory behavior, excluding positive solutions through a comparative analysis with second-order equations. Chapter 5 extends the analysis to higher-order functional differential equations in the non-canonical case. Introducing a unique two-condition criterion, the chapter establishes conditions for the oscillation of all solutions, improving upon existing literature. The final chapter, Chapter 6, summarizes the thesis by providing a comprehensive conclusion and outlining avenues for future work. Overall, the thesis contributes valuable insights and criteria to the study of neutral differential equations, particularly in understanding their asymptotic and oscillatory behavior.