Oscillation of linear difference equations with deviating arguments

The following difference equation with deviating arguments: is considered, where Δu(k) = u(k + 1) − u(k), Δ2 = Δ ° Δ, pj (j = 1, …, m) is a sequence of nonnegative numbers, σj : → and limk → + ∞ σj(k) = + ∞ (j = 1, …, m). In the paper, sufficient conditions are established for all proper solutions of the above equation to be oscillatory.