On the asymptotic and oscillatory behavior of solutions of second order nonlinear neutral difference equations. (English) Zbl 0862.39007

The paper deals with neutral difference equations of the form \[ \Delta^2(y(n)+p(n)y(n-k))- F(n,y(n-\sigma_1),\dots,y(n-\sigma_m))=0,\quad n\in\mathbb{Z}, \] where \(\{p(n)\}\) is a real sequence and \(k,\sigma_1,\dots,\sigma_m\) are nonnegative integers. Under suitable conditions on the function \(F:\mathbb{Z}\times\mathbb{R}^m\to\mathbb{R}\) the asymptotic properties of nonoscillatory solutions of this equation are studied and sufficient conditions are given for all bounded solutions to be oscillatory. The theoretical results are illustrated by means of a number of examples.


39A12 Discrete version of topics in analysis
39A11 Stability of difference equations (MSC2000)