Linearized Comparison Criteria for a First Order Nonlinear Neutral Delay Difference Equation

IIn this paper, we consider a class of first order nonlinear neutral delay difference equations with variable coefficients of the form Δ [x(n) - P (n)x(n - T (n))] + Σ sub j=1 /sub sup m /sup Q sub j /sub (n)f sub j /sub (x(n - σ sub j /sub (n))) = 0, n ≤ n sub 0 /sub .(*) We establish sufficient conditions for oscillation of all solutions of (*) and a linearized comparison theorem is derived which establishes a connection between our nonlinear equations and a class of linear neutral equations with constant coefficients.