Study On Several Kinds Of Difference Equations

With the development of science and technology in physics,economics and many other animal species,natural science and the edge of science puts forward specific mathematical models described by difference equations.It can be said that the differential equation is a powerful tool used to describe the variation of natural phenomenon.However due to the true solution is very difficult,so to investigate the properties of solution in theory has been a hot topic in recent research.This paper studies two problems are of two order linear differential equation oscillation and a first-order two-dimensional linear difference equations.The solution of the two problems,prove to supplement and amend some theorems and conclusions are,for some oscillation theorems for modification get the oscillation criteria under the new conditions.The main research works are summarized as follows:First of all,introduced to the study background,research and research significance,and summarizes the basic theory related to the differential equation of related concepts and knowledge of mathematics.Secondly,the two order linear oscillation of difference equations.By using integral,indefinite integral,convergence,inequality and theorem proving process theory,two order linear on the oscillation criteria for difference equations were modified,reasoning ideas different from other scholars,obtained on the two order linear difference equations of the vibration of the other criterion.Finally,a first-order linear oscillation of difference equations.By using the integral inequality theorem,Stolz theorem,the first-order differential equation of two-dimensional linear oscillation theorem of condition is modified,perfected a first-order linear differential equation of vibration theory.