Oscillation criteria for a class of higher odd order neutral difference equations with continuous variable

In this paper, we are mainly concerned with oscillatory behavior of solutions for a class of higher odd order nonlinear neutral difference equations with continuous variable. By converting the above difference equations to the corresponding differential equations and inequalities, the oscillatory criteria are obtained. In addition, examples are given to illustrate the obtained criteria, respectively

Oscillation criteria for even-order nonlinear neutral difference equations with continuous variables

In this article, we study the oscillatory behavior of solutions to even-order nonlinear neutral difference equations of the form $$\Delta^m_\tau( x(t)-px(t-r))+f(t,x(g(t)))=0.$$ Using an integral transformation, the Riccati transformation, and iteration, we obtain sufficient conditions for all solutions to be oscillatory. Examples are also given to illustrate the obtained criteria