Oscillation and Asymptotic Stability of Difference Equations Depending on Parameters*

In this paper we study oscillation and asymptotic stability of the difference equation of the form where a, b and c are real parameters, τ and σ are positive integers. We find the asymptotically stable domain of this equation. When the tuple (a, b, c) belongs to this domain, the equation is asymptotically stable and the inverse is also true. In addition, we provide necessary and sufficient conditions for the equation to be oscillatory.