The oscillation of higher-order nonlinear difference equations. (Q1767233)

Oscillatory properties of the solutions of \[ \triangle^mx_{n-1} + f(n, x_{\tau(n)}) = 0, \] \[ \triangle^mx_{n-1} + f(n, x_n) = 0, \] are studied, where \(m\geq 2\), \(\tau:{\mathbb N}\rightarrow {\mathbb N}\) is such that \(\lim_{n\rightarrow\infty}\tau(n) = \infty\), \(| n-\tau(n)| \leq M\), \(\forall n\geq 0\), \(M\) being some positive integer. Here \(f(n,\cdot)\) is nondecreasing and \(xf(n,x)>0\) for \(x\neq 0\).