Oscillation Criteria for Higher Order Nonlinear Generalized Neutral Difference Equations

TL;DR

This paper establishes oscillation criteria for high order nonlinear generalized neutral difference equations, providing conditions under which solutions oscillate, thereby advancing the understanding of their dynamic behavior.

Contribution

It introduces new oscillation criteria specifically for high order nonlinear generalized neutral difference equations, extending existing theories.

Findings

Derived sufficient conditions for oscillation of solutions.

Extended oscillation theory to higher order neutral difference equations.

Provided examples illustrating the application of the criteria.

Abstract

In the present study we highlight some results related to the oscillation for high order nonlinear generalized neutral difference equation in the following form \begin{equation*} \Delta_{\ell}\left(a(k)\Delta_{\ell}^{m-1}z(k)\right)+q(k)f(x({k-\rho\ell}))=0, \label{1e} \end{equation*} where $z(k)=x(k)+p(k)x({\tau(k)})$.