Research On The Theory Of Oscillation And Nonoscillation Of Neutral Partial Difference Equations

In this paper, we discuss the oscillation and nonoscillation of the solutions of the neutral partial difference equations. It is composed of three chapters.Chapter 1, we simply introduce some known results about partial difference equations and the main content of this paper.Chapter 2, we investigate the existence of multiple positive solutions of the neutral partial difference equations on the base of the existed results of partial difference and difference equations, and obtain some sufficient conditions for the existence of multiple positive solutions. This result extend some criteria obtained by the the forefather.Chapter 3, we consider the oscillation of the boundary problems of neutral parabolic partial difference equations. Some results for neutral functional parabolic equations are extend to neutral parabolic partial difference equations, some sufficient and necessary conditions under which every solution of the equations is oscillatory, are obtained.