The Study Of Oscillatory Theory Of Higher-Order Difference Equations And Second-Order Dynamic Equations On Time Scales

With the rapid development of science and technology, many mathematical models which are described by differential equations and difference equations are applied in both natural science and edging fields such as physics, population dynamics, theory of control, biology, medicine, economics, etc. Dynamic equations on scales which have received closed attention in recent years, as well as differential equations and difference equations, are powerful tools in describing the phenomena and laws of the nature. Since it is too difficult to give the general solutions of the equations, there has been an increasing interest in the investment of the properties of the solutions.According to the contents, this thesis is divided into three chapters as follows:In chapter one, we introduce a survey to the background and the current development of the difference equations and dynamic equations on time scales.In chapter two, we discuss the oscillation and the existence of nonoscillatory solutions of odd-order difference equations with nonlinear neutral terms. Some new criteria are established. Furthermore, some examples are given to illustrate the advance of the results.In chapter three, we investigate the oscillatory criteria for second-order self-adjoint dynamic equations with "integral small" coefficient, by using Riccati transformation, some criteria are established.