OSCILLATION OF FIRST ORDER LINEAR NEUTRAL DELAY DIFFERENCE EQUATIONS WITH CONSTANT AND VARIABLE COEFFICIENTS

In this paper, we consider the first order neutral delay difference equations with variable coefficients of the form []1( )()( ) ()0,mkkkx npx nq n x n=∆+− τ +− σ=∑0,n≥ (*) where p is a real number, {}0( )knq n∞=is a sequence of nonnegative real numbers which are not identically zero, and m, τ and σk (k=1, 2, . . . , m) are positive integers. We establish sufficient conditions for all solutions of (*) are oscillatory when −e−τ < p ≤ 0 and for the existence of nonoscillatory solution for (*) when p=0.