Oscillations of higher-order neutral difference equations
The authors investigate the oscillatory behavior of the solutions of an order \(m\) nonlinear neutral difference equation of the form \[ \Delta^m(y_n+p_ny_{n-k})+q_nf(y_{n-l})=0,\quad n\in\mathbb{N}=\{0,1,\ldots\}, \] where \(\Delta\) is the usual forward difference operator defined by \(\Delta y_n=y_{n+1}-y_n\), \(k\), \(l\) are nonnegative integers, \(\{p_n\}\), \(\{q_n\}\) are real sequences with \(q_n\geq 0\), \(n\in\mathbb{N}\), and \(f:\mathbb{R}\to\mathbb{R}\) is continuous with \(uf(u)>0\), for all \(u\neq 0\). Some sufficient conditions are given which ensure that all solutions of the above equation are oscillatory.
scientific article; zbMATH DE number 1078539