Comparison Theorems and Oscillation Criteria for Difference Equations1

First, we establish the equivalence of the oscillation of the delay difference equation D xnqpnxnyks0, and the second-order difference equation kq1.k k k D2 yny1q2 k kq1 pny kq1.kq1 yns0, where pn4is a sequence of nonnegative real numbers and k is a positive integer. Next, we obtain some sharp conditions for oscillations and nonoscillations of the first equation