Oscillation Of First Order Neutral Difference Equations With Continuous Arguments

In this paper . we are mainly concerned with oscillation of solutions of the following first order neutral difference equations with continuous arguments of the formwhere denote m = max = min qi(s).First, several lemmas are given by using the integral transformations, so that the difference equations are converted into the corresponding differential equations and inequalities, and some important properties of new variable are obtained. Then .with the help of some good results of differential equations theory, some sufficient conditions for all solutions of the equations to be oscillatory are obtained. The way is to proof by contradiction and construct sequence.