A final result on the oscillation of solutions of the linear discrete delayed equation δ x (n) = - P (n) x (n - K) with a positive coefficient

A linear (k + 1) th-order discrete delayed equation Δ x (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 → ∞.