Qualitative Properties Of Solution Of Partial Difference Equations-Oscillations

In this dissertation, we mainly consider the qualitative properties of solutions of some partial difference equations-—oscillations of solutions. Criteria on the oscillations are obtained. In this Dissertation we have five parts.In the first part, we introduce some concepts of difference equations. From this, we give the reasons that difference equations are considered and the usually steps construction of the ordinary difference equations. In addition to we introduce the concepts and definitions of oscillation of solutions for partial difference equations. From the example, we are more acquainted with the oscillations of solutions of the partial difference equations.In the second part, we mainly consider oscillations of solution of some linear and nonlinear partial difference equations with discrete variables and delays. We give the concepts and the definitions and obtain the criteria of oscillations of solution of these partial differnce equations. Firstly, we obtain the criteria of oscillations of solution of partial differnce equations with constant cofficients and delays. In the proof, using the z — translating we obtain the criteria of oscillation of solution of these simple partial difference equations. Secondly, we introduce the criteria of system of partial difference equations. Since the difficulty in studying of this system, we consider the simple system with constant coefficients. But for the complex system, they are still under invistigation. Thirdly, we talk about system of the variable coefficients of partial difference equations. On the basis of constant coefficients, we properly confirm with the variable coefficients and obtain corresponsal criteria. Finally, we consider the criteria of the nonlinear partial difference equations with discrete variables. The maily method is contrary method. We can obtain the relationship between the positive solutions of equation through studing theproperties of the sequence {A_mn} for the large m,n. We can obtain the criateria of theoscillations using the maximum or minimum values.In the third part, we maily consider some linear or nonlinear partial difference equation with continuous variables and delays and obtain the criteria of the oscillations. Firstly, we consider the system with constant coefficienta. It is similar to the system of discrete with constant coefficients. Only there is a different translation. We use the Laplace translation about the continuous system. The same as the second part, we use method of contrary proof and obtain the criteria of the...