An improvement for oscillation of first order difference equations.

In this article, we examine the first-order retarded difference equation ∆v(n) + ^m ∑_i=1p_i(n)v (δ_i(n)) = 0, n ≥ 0, where (δ_i(n))(i = 1, . . ., m) are sequences of positive real numbers such that δ_i(n) ≤ n for n ≥ 0, and lim_n→∞ δ_i(n) = ∞ and (p_i(n))(i = 1, . . ., m) are sequences of nonnegative real numbers, When the delay terms δ_i(n) are not necessarily monotone, we will give an oscillation criterion obtained for the differential equation, but not yet obtained for its discrete analogous. Finally, we give an example to illustrate our result. [ABSTRACT FROM AUTHOR]