Boundedness and asymptotic properties of solutions of some linear and sublinear delay difference equations

This paper discusses some asymptotic properties of the delay difference equation Δ y ( n ) = a ( n ) y ( n ) + ∑ i = 1 k b i ( n ) | y ( τ i ( n ) ) | r i sgn y ( τ i ( n ) ) , 0 < r i ≤ 1 . First, we briefly mention some known qualitative properties of this equation. Further, as the main result, we present an asymptotic estimate of its solutions which is derived in the case not considered by the other authors. Applications of this result to particular cases conclude the paper.