Oscillation theorems for second order neutral difference equations
Oscillation criteria for the second order difference equations of the type \[ \Delta^ 2x_ n+q_ nf(x_{n-r})=0 \] and the neutral difference equation \[ \Delta^ 2 (x_ n + px_{n-\delta k}) + q_ n f(x_{n-r})= 0 \] are given. Here \(\Delta x_ n = x_{n+1}-x_ n\), \(\delta = \pm 1\), \(p\) is a real number, \(r\) and \(k\) are nonnegative integers, \(\{q_ n\}\) is a sequence of nonnegative real numbers, and \(f:\mathbb{R} \to \mathbb{R} = (-\infty,\infty)\) is a continuous function.
scientific article; zbMATH DE number 566118
scientific article