Oscillation Of Nonlinear Differential Equation With Multiple Time-varying Delays

This paper discusses the oscillation of nonlinear delayed differential equations. It is well known that the oscillation theory is an important branch of differential equations. Oscillation has become a very active research area. In recent decades, while the theories in various areas of differential equations are developing, tremendous progress are also obtained whatever studies from linear to nonlinear or from first order to n-order, or even the discussion on the infinite order.In this paper,the oscillation of nonlinear differential equations with multiple time-varying delays is discussed and some results are obtained.The paper is organized as follows:The first chapter introduces the research situation of delayed differential equations and the detrusion of the concept on oscillation. The introduction on oscillation by Profes-sor Zhang Binggen and the research on oscillation of a kind of neutral delayed differential equations by Yu Jianshe and Tang Xianhua are briefly explained.In chapter two, some necessary preliminaries are given. The background of nonlinear delayed differential equations, the concept on oscillation of solution and the theory which decides the oscillation of a kind of nonlinear differential equations are introduced, especially the oscillation theory of Logistic equations.In the third chapter, the oscillation on two kinds of nonlinear differential equations with multiple time-varying delays is mainly discussed and some results are obtained in virtue of the theory of linear delayed differential equations and approximative delayed differential equations.