A Final Result on the Oscillation of Solutions of the Linear Discrete Delayed Equation Δx(n)=−p(n)x(n−k) with a Positive Coefficient

Abstract

A linear (k+1)th-order discrete delayed equation Δx(n)=−p(n)x(n−k) where p(n) a positive sequence is considered for n→∞. This equation is known to have a positive solution if the sequence p(n) satisfies an inequality. Our aim is to show that, in the case of the opposite inequality for p(n), all solutions of the equation considered are oscillating for n→∞.