Oscillations of difference equations with non-monotone retarded arguments

Consider the first-order retarded difference equation 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))(n >= 0) is a sequence of integers such that tau(n) <= n-1, n >= 0; and lim(n ->infinity)tau(n) = infinity . Under the assumption that the retarded argument is non- monotone, a new oscillation criterion, involving lim inf, is established. An example illustrates the case when the result of the paper implies oscillation while previously known results fail. (C) 2015 Elsevier Inc. All rights reserved.