Oscillation Of Some Classes Of Neutral Delay Differential Equations

In the study of the oscillation theory of delay differential equations, oscillation theory has important practical significance and research value. Besides, neutral differential equa-tions with delays have general applications in the disciplines of natural and social science. For example, the majority of mathematical models are usually appeared in medical science, epidemiology, genetic problems and practical problems, such as the law of population quan-tity change. Therefore, it is particularly important to the study of the oscillation of neutral differential equations with delays.This paper mainly discuss the oscillation of three kinds of neutral delay differential equations.Firstly, Chapter 1 introduces the research significance and the research background of neutral differential equations with delays, then introduces our research contents of this paper.In Chapter 2, we consider the oscillation of a class of two-order neutral differential equation with positive and negative coefficients and many variable delays By using generalized Riccati transformation, we obtain several sufficient conditions that ensure the oscillation of the above equation.In Chapter 3, we discuss the oscillation of a general three-order neutral delay differential equation with positive and negative coefficients Our results generalize the corresponding results in some existing literatures.In Chapter 4, we study the oscillation of a class of three-order neutral differential equation with distributed delays By using the general Riccati transformation and Hardy inequality method, we obtain several sufficient conditions to ensure the oscillation of this equation.