Some results on the behavior of the solutions of a linear delay difference equation with periodic coefficients

Abstract

Some new results on the asymptotic behavior, the nonoscillation and the stability of a class of linear delay difference equations with periodic coefficients and constant delays are given. The coefficients have a common period and the delays are multiples ,of this period. The results are obtained via a positive root of an associated equation, which is in a sense the corresponding characteristic equation. The application in the special case of constant coefficients of the results obtained is also presented.

Keywords:

• Difference equation
• periodic coefficients
• solution
• asymptotic behavior, nonoscillation