Non-Oscillatory Solutions of Higher Order Nonlinear Neutral Delay Difference Equation

Abstract

Consider the forced higher order nonlinear neutral delay difference equation L_m( x(n) + cx(n - τ) ) + F ( n, x(σ(n) ) ) = g(n), (n ≥ n_0). We obtain a global result (with respect to c), which consists of some sufficient conditions for the existence of a non-oscillatory solution of the above equation. Our results improve and extend a number of existing results.