Existence of non-oscillatory solutions to higher-order mixed difference equations

Abstract

In this paper, we consider the higher order neutral nonlinear difference equation Δm (x(n) + p(n)x(τ(n))) + ƒ1(n, x(σ1(n))) - ƒ2(n, x(σ2(n))) = 0, Δm (x(n) + p(n)x(τ(n))) + ƒ1(n, x(σ1(n))) - ƒ2(n, x(σ2(n))) = g(n), Δm (x(n) + p(n)x(τ(n))) + Σli=1 bi(n)x(σi(n)) = 0. We obtain sufficient conditions for the existence of non-oscillatory solutions.