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Consider the first-order delay difference equation with a constant argument Δxn+pnxn-k=0, n=0,1,2,…, and the delay difference equation with a variable argument Δxn+pnxτn=0, n=0,1,2,…, where p(n) is a sequence of nonnegative real numbers, k is a positive integer, Δx(n)=x(n+1)-x(n), and τ(n) is a sequence of integers such that τ(n)≤n-1 for all n≥0 and limn→∞τ(n)=∞. A survey on the oscillation of all solutions to these equations is presented. Examples illustrating the results are given.

Oscillation Conditions for Difference Equations with a Monotone or Nonmonotone Argument