Oscillation results of higher order nonlinear neutral delay difference equations with a nonlinear neutral term

Abstract

In this work, we shall consider higher order nonlinear neutral delay difference equation of the type ∆m [xn + pnx α n−k] + qnx β n−l = 0 , n = 0, 1, 2, ... where {pn} is a sequence of real numbers, {qn} is a sequence of nonnegative real numbers, k and l are positive integers and α, β ∈ (0, ∞) are quotient of odd positive integers. We obtain sufficient conditions for the oscillations of all solutions of this equation.