Oscillatory properties of third-order semi-noncanonical nonlinear delay difference equations

Abstract

We study the oscillatory properties of the solutions of the third-order nonlinear semi-noncanonical delay difference equation D3y(n) + f(n)y (σ(n)) = 0, where D3y(n) = ∆(b(n)∆(a(n)(∆y(n)) )) is studied. The main idea is to transform the semi-noncanonical operator into canonical form. Then we obtain new oscillation theorems for the studied equation. Examples are provided to illustrate the importance of the main results.