"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."
The authors present Kneser-type oscillation criteria for a class of advanced type second-order difference equations. The results obtained are new and they improve and complement known results in the literature. Two examples are provided to illustrate the importance of the main results.
In this paper, we present a new method to establish the oscillation of advanced second-order difference equations of the form Δ η ℓ Δ υ ℓ + ρ ℓ υ σ ℓ = 0 , using the ordinary difference equation Δ η ℓ Δ υ ℓ + q ℓ υ ℓ + 1 = 0 . The obtained results are new and improve the existing criteria. We provide examples to illustrate the main results.
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