Oscillations of delay difference equations in a critical state

Consider the first-order delay difference equation in the case where lim infn→∞ Pi(n) = pi ≥ 0, ki > 0, I = 1,2,…. A necessary and sufficient condition for the oscillation of all solutions of the above equation is established in the critical state that the corresponding “limiting” equation admits a nonoscillatory solution. It is to be pointed out, that there is no result in this critical state for a delay difference equation with more than one delay argument.