| Followed by the swift development of the research worlds concerning numerical calculation, computer science, information science, auto-control technology and so on, many mathematic models described by difference equations was arose, which means that the research about the stability of difference equations with delays looks like increasingly important.The present paper employs the classical notions in stability, proceed some certain advancement concerning the initial difference equations, and discuss the condition to the zero stability of the two classes of the equations.The thesis is divided into three sections according to contents.Chapter1In preference, we introduce the main contents of this paper.Chapter2In chapter2, We consider the stability of the following class of differ-ence equations with infinite delays: and make the zero solution of the above equation globally asymptotically stable, which improve the stability conditions about the linear and nonlinear equations. Because the equation is infinite delay one, the initial dataΦj,—∞<j<0are directly dependent on each xi+1i≥0, and the stability analysis becomes very complicated compared with the case of finite delays.Chapter3In this chapter, we consider the sufficient conditions for asymptotic stability and instability of certain higher order nonlinear difference equations with finite delays in finite-dimensional spaces. where y(k) E X, X is a Banach space; g(.) is a function on Z2×Xr-1→X and (.) is a function on Z x Xr+1→X. With the aid of the general comparison condition on the right-hand side function f(k,.), we generelize the stability and instability result. |
