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 D_3y(n)+f(n)y^\beta(\sigma(n))=0, where $D_3 y(n)=\Delta(b(n)\Delta(a(n)(\Delta y(n))^\alpha))$ 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.

Keywords

• semi-noncanonical operator
• third-order
• delay difference equation
• oscillation