The Study Of Asymptomatic Behavior On A Class Of High Order Neutral Functional Differential Equation

The qualitative theory of functional differential equations is an effective tool to describe the law of society development. In recent years, many secific mathematical models, which are described by the theory of differential equations, have been put forward in different areas, such as mechanics, biomathematics, economic mathematics, communication theory. Tthe oscillation, as an important part of qualitative theory of functional differential equationst, is not only of great theoretical significance, but also has some practical significance for the human society development.In this paper, we study the vibration behavior of a class of Higher Order Neutral Functional Differential Equations, as follows:In chapter 1, we simply outline the background and present situation of oscillation of functional differential equations at home and abroad;In chapter 2, we introduce the definition related to the oscillation of functional differential equations and the important theorem and inequality required in the proof of oscillation;In chapter 3, we discuss the vibration behavior of n (n?3) order neutral differential equations, abtain asymptotic behavior of nonoscillatory solutions x(t) of the equation, get some new conclusion about vibration criteria by applying generalized Riccati transformation, integral averaging technique of Philos-type, Young inquality, Schwartz inequality, H(?)lder inequality etc, and improve and generalize known results in literature.