"Oscillations of second-order noncanonical advanced difference equations via canonical transformation"

Abstract

"This paper introduces a new improved method for obtaining the oscillation of a second-order advanced difference equation of the form \begin{equation*} \Delta(\eta(n)\Delta\chi(n))+f(n)\chi(\sigma(n))=0 \end{equation*} where $\eta(n)>0,$ $\sum_{n=n_0}^{\infty}\frac{1}{\eta(n)}<\infty,$ $f(n)>0,$ $\sigma(n)\geq n+1,$ and $\{\sigma(n)\}$ is a monotonically increasing integer sequence. We derive new oscillation criteria by transforming the studied equation into the canonical form. The obtained results are original and improve on the existing criteria. Examples illustrating the main results are presented at the end of the paper."