Oscillation theorems for third order nonlinear delay difference equations

Abstract

Sufficient conditions are obtained for the third order nonlinear delay difference equation of the form \Delta(a_n(\Delta(b_n(\Delta y_n)^{\alpha})))+q_nf(y_{\sigma(n)})=0 to have property ${(\rm A)}$ or to be oscillatory. These conditions improve and complement many known results reported in the literature. Examples are provided to illustrate the importance of the main results.

Keywords

• third order delay difference equation
• property ${(\rm A)}$
• comparison theorem