Some qualitative behavior of solutions of general class of difference equations

Abstract

In this work, we consider the general class of difference equations (covered many equations that have been studied by other authors or that have never been studied before), as a means of establishing general theorems, for the asymptotic behavior of its solutions. Namely, we state new necessary and sufficient conditions for local asymptotic stability of these equations. In addition, we study the periodic solution with period two and three. Our results essentially extend and improve the earlier ones.