A Survey on the Oscillation of Solutions of First Order Delay Difference Equations

Abstract

In this paper, a survey of the most interesting results on the oscillation of all solutions of the first order delay difference equation of the form

x_n+1 − x_n + p_nx_n−k = 0,          n= 0, 1, 2, ...,

where {p_n} is a sequence of nonnegative real numbers and k is a positive integer is presented, especially in the case when neither of the well-known oscillation conditions

   and 

is satisfied.