| The theory of oscillation is an important branch of the qualitative theory of differential equations. In the field of modern applied mathematics, it has made considerable headway in recent years, because all the structures of its emergence have deep physical background and realistic mathematical models. Many scholars take on the research of this field, they have achieved many good results. With the increasing development of science and technology, there are many problems relating to differential equation derived from lots of real applications and practice, such as whether differential equation has a oscillating solution or not, and whether all of its solutions are oscillatory or not. In very resent years, great changes of this field have taken place. Especially, the second order superlinear differential equation has been paid more attentions and investigated in various classes by using different methods(see [1]-[36]).The present paper employs a generalized Riccati transformation, Integral average technique and the monotone of functions to investigate the oscillation criteria for some class of neutral equations with distributed deviating argu-ment, the results of which generalized and improved some known oscillation criteria.The thesis is divided into three sections according to contents.In Chapter 1, Preface, we introduce the main contents of this paper.In Chapter 2, we study the oscillation criteria for even order neutral equa-tions with distribute deviating argument, we mainly employed a generalized Riccati transformation and Integral average technique shall further the investigation and improve the main results of Zhao [37] and Wang [38], we obtained several new oscillation criteria at the end of this section.In Chapter 3, In this chapter, using a generalized Riccati transformation and developing ideas exploited by Yuri V. Rogovchenko and Tuncay [42], we establish some new oscillation criteria for Eq which remove condition (C2)in Theorem A and (C5) in Theorem B in Wang[41].
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