Delay Stability Of Linear Ordinary Differential Equations

Difference equation is one of main tools of studing differential equation.Recently, there has appeared many new directions in the research of difference equation theory. Especially, it is one of the focus research of difference equation theory to find stability criterions of the solution of a difference equation.By using root-analysis for the characteristic eqution, this paper provides necessary and sufficient conditions for the asymptotic stability of the zero solution of three classes of linear delay difference equations:Where the coefficients b,d are nonzero real numbers, p is a real number and k,l,N are positive integers with k > (N－1)l, These results are represented by coefficients of difference equations, which will be convenient for applications and verify.