The Oscillation For Several Class Of Neutral Dynamic Equations On Time Scales

The theory of time scales, which has been received much attention, was intro-duced by Stefan Hilger in his Ph.D. Thesis in 1988. But few studies consider the nonlinear neutral dynamic equations and dynamic systems on time scales.The paper consists of four chapters.In chapter one,we give a brief introduction to the time scales calculus.In chapter two,based on the results of oscillation theory for differential equa-tions and difference equations, we mainly consider the oscillation of a class neutral dynamic equation with several delays on time scales, and obtain some sufficient conditions for every solution of the equation which is oscillatory.Furthermore,we study the existence of non-oscillatory solutions of the neutral delay dynamic equa-tion with positive and negative cofficients on time scales, and obtain some sufficient conditions for non-oscillatory solutions existence.In chapter three, we have got some interesting results about the oscillation of solutions for the high neutral dynamic equation.In the last chapter,we mainly study the oscillatory behavior of solution for the dynamic system,and obtain some sufficient conditions for oscillation and non-oscillation.