OSCILLATORY PROPERTIES OF THIRD-ORDER SEMI-NONCANONICAL NONLINEAR DELAY DIFFERENCE EQUATIONS.

We study the oscillatory properties of the solutions of the third-order nonlinear semi-noncanonical delay difference equation D3y(n) + f(n)y^β(-(n)) = 0, where D3y(n) = Δ(b(n)Δ(a(n)(Δy(n))^α)) 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. [ABSTRACT FROM AUTHOR]