Existence of nonoscillatory solutions of higher-order neutral difference equations with general coefficients (Q1861797)

The main result of the paper provides a sufficient condition for the existence of a nonoscillatory solution of the higher order difference equation \[ \Delta^m(x_n+cx_{n-k})+p_n x_{n-r}=0,\qquad n=n_0, n_0+1, n_0+2,\dots, \] where \(c\in\mathbb R\), \(m\geq 1\) is an odd integer, \(k\geq 1\), \(r\geq 0\) are integers, \(\{p_n\}_{n=n_0}^\infty\) is a sequence of real numbers and \(\Delta\) denotes the forward difference operator, \(\Delta x_n=x_{n+1}-x_n\).