Oscillation of retarded difference equations with a non-monotone argument

This paper concerns the oscillatory behaviour of the first-order retarded difference equation of the form Delta x(n) + p(n) x(tau(n)) = 0, n is an element of N-0, where (p(n))(n >= 0) is a sequence of nonnegative real numbers and tau(n) is a (not neccesarily monotone) sequence of integers such that tau(n) <= n-1, for n is an element of N-0 and lim(n ->infinity) tau(n)=infinity. Sufficient oscillation conditions, involving lim sup, are established. The results obtained improve known results existing in the literature and examples illustrating the significance of these results are provided.