Abstract
A comparison theorem on oscillation behavior is firstly established for a class of even-order nonlinear neutral delay difference equations. By using the obtained comparison theorem, two oscillation criteria are derived for the class of even-order nonlinear neutral delay difference equations. Two examples are given to show the effectiveness of the obtained results.
Highlights
There have been a lot of research papers in connection with the oscillation of solutions of difference equations with or without neutral terms
Stavroulakis studied the oscillatory behavior of all solutions of first-order delay difference equation
there have been a lot of research papers in connection
Summary
There have been a lot of research papers in connection with the oscillation of solutions of difference equations with or without neutral terms. In 2004, Stavroulakis [4] studied the oscillatory behavior of all solutions of first-order delay difference equation, xn+1 − xn + pnxn−k = 0,. Thandapani et al [5] studied the oscillatory behavior of all solutions of second-order neutral delay difference equation, Δ2 (yn − pyn−k) − qnf (yn−t) = 0,. In 2000, Zhou et al [6] studied the oscillatory behavior of all solutions of even-order neutral delay difference equation, Δm (xn − png (xn−k)) − qnh (xn−l) = 0,. The studies on oscillatory behavior of all solutions of even-order delay difference equations, we recommend referring to [7–10].
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