Oscillation And Nonoscillation Of Solutions Of Difference Equations With Impulses

This paper is composed of three chapters, which respectively discusses the following impulsive delay difference equations with discrete variables and continuous variables:In chapter 1, we investigate the oscillation and nonoscillation of equation (I) and some sufficient conditions for oscillation and nonoscillation are obtained. Consequently we extend these results to the difference equations with several delays and with nonlinear impulsive perturbations and with variable delays respectively.In chapter 2, some new results are gained by extending some results in chapter 1 to the discrete impulsive difference inequalities. These new results are applied to the neutral impulsive difference equation (II) with discrete variables and sufficient conditions for oscillation of these equations are obtained.Finally, in chapter 3, we apply related methods and results in chapter 1 and 2 to the impulsive difference equation (III) and (IV) with continuous variables and gain the sufficient conditions for their oscillation. These results are also extended to the equation with several delays corresponding equation (III)All results on oscillation above are suitable for the difference equations without impulses, so some results of related paper are extended.