Oscillation Of Two Kinds Of The Second Order Nonlinear Neutral Differential Equations With Delay

Oscillation theory of ordinary differential equations in the theory of differential equations is an important branch. It was arrived from the second order linear ordinary differential equation by Sturm in 1836. In recent years, the study of the oscillation of solutions for differential equations is very active. The application of this theory in the field of mathematics has been achieved rapid development and extensive attention. Oscil-lation of differential equations get rich results whether from the linear equations to nonlinear equations or from the low order equations to high order equations. Re-cently, the research of this theory has also been extended to functional differential equation, differience equation, partial functional differential equation, matrix differ-ential equation and ecology mathematics by many domestic and foreign scholars. The theory has profound application specially in biological model and economical model, so it has high practical value. For example, an important delay Logistic equation of signal cenospeciesAmong it, (?) includes several influences to increase of cenospecies.This paper is composed by three chapters, we study the oscillation of two kinds of the second order nonlinear neutral differential equations by classical technique of Riccati, method of integral average and method of functional average.In the first Chapter, we mainly introduce the background and development for the oscillation theory of differential equations. Then we give a brief introduction on mine. In the second Chapter, we discuss the oscillation of the second order neutral delay differential equation and get three sufficient conditions.In the third Chapter, we discuss the oscillation of the second order nonlinear neutral functional differential equation with delayAt last, we put some problems related to oscillation theory of differential equa-tion in the future.