Existence Of Solutions Of Several Classes Of Neutral Dynamic Equations With Time Delay On Time Scales

In recent years, more and more people put attention to the existence of nonoscil-latory solutions and oscillatory solutions of neutral dynamic equations with time delay on time scales. In this paper, we study the existence of nonoscillatory solu-tions and bounded oscillatory solutions of second order neutral dynamic equations with time delay on time scales, and the existence of nonoscillatory solutions and oscillatory solutions of higher order neutral dynamic equations with time delay on time scales. There are five chapters in this paper.In Chapter 1, we introduce the fundamental concepts and theory of time scales.In Chapter 2, by Krasnoelskii fixed point theorem we study the existence of nonoscillatory solutions of the forced second order neutral dynamic equation with time delay on time scales as following where T is an unbounded time scale.In chapter 3, by Banach fixed point theorem we study the existence of nonoscil-latory solutions of the forced higher order neutral dynamic equation with time delay on time scales as following where T is an unbounded time scale.In chapter 4, we study the existence of bounded oscillatory solutions of the forced second order neutral dynamic equation with time delay on time scales as following where z(t)= x(t)+p(t)x(T(t)), where T is an unbounded time scale.In chapter 5, we discuss the following higher order neutral dynamic equation with time delay on time scales, and get the results of oscillation of this equation when n is odd order and even order, where T is an unbounded time scale.