Oscillation For Some Kinds Of Difference Equations With Continuous Arguments

Difference equations are important tools in technology and ecnomy research,the oscillation theory has got many scholar's attention. In recent years,people bring broad interest on oscillation for difference equations with continuous arguments,and obtained by all means evolvements.This paper traverse the oscillation for two kinds of difference equations with continuous arguments,including oscillation for nonlinear neutral difference equations with continuous arguments, oscillation for impulsive several delays difference equations with continuous arguments, several sufficient conditions for oscillation are obtained. Some results in the previous papers are expanded and improved.Accordingly,this paper has broader application.First, the thesis studies the oscillation for nonlinear neutral several delays difference equations with continuous arguments, researches the connection on oscillation between the equation and opposite discrete system or delay differectial equations. At the same time, we study the connection on oscillation between nonlinear equations and the opposite linear equations, some existing results in the literatures are improved.Then, as to the oscillation for the impulsive delay difference equations with continuous arguments. Using the method of construct function, we get an assistant equation, which is opposite with the impulsive delay difference equations with continuous arguments. We strike up equivalence on oscillation between the two equations, with this way, we can know the oscillation for impulsive delay difference equations merely with studying oscillation for the assistant function. Make use of the method, several sufficiency conditions on oscillation for impulsive delay difference equations with continuous arguments are obtained. Finally, with the same method, we study the impulsive neutral delay difference equations with continuous arguments, two sufficiency conditions are obtained. These conclusions on oscillation for difference equations without impulsive can be regarded as expanded and improved in impulsive condition.