The oscillation of higher-ordernonlinear difference equations Original Research Article

The authors discuss the relation of the oscillation of the following two difference equations, View the MathML sourceΔmxn−1+f(n,xn)=0,Δmxn−1+f(n,xτ(n))=0, Turn MathJax on where m ≥ 2, τ : N → N, N isthe set of integers, |n − τ(n)| ≤ Mfor n ∈ N0, M is a positive integer, View the MathML sourcelimn→∞τ(n)=∞,f:N×R→R,f is nondecreasing in x, xf(n, x)> 0, as x ≠ 0. Wewill show some relations of the oscillation of the above two equations. Especially, for m to be even, we establish the equivalenceof the oscillation of the above two difference equations.