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Some oscillation theorems for perturbed nonlinear difference equations. (English) Zbl 0847.39009

Corduneanu, C. (ed.), Qualitative problems for differential equations and control theory. Dedicated to Aristide Halanay on occasion of his 70th birthday. Singapore: World Scientific. 315-320 (1995).
The aim of this paper is to investigate the oscillatory behavior of solutions of general perturbed second-order nonlinear difference equations of the form \[ \Delta(a_n \Psi(n, y_{n+ 1}, \Delta y_n) \Delta y_n)+ Q(n, y_{n+ 1})= P(n, y_{n+ 1}, \Delta y_n),\quad n\in \mathbb{N}, \] where \(\mathbb{N}= \{0, 1, 2,\dots\}\), \(\Delta\) is the forward difference operator defined by \(\Delta y_n= y_{n+ 1}- y_n\), \(\{a_n\}\) is a real sequence with \(a_n> 0\) for all \(n\in \mathbb{N}\), \(\Psi: \mathbb{N}\times \mathbb{R}^2\to \mathbb{R}\), \(Q: \mathbb{N}\times \mathbb{R}\to \mathbb{R}\), and \(P: \mathbb{N}\times \mathbb{R}^2\to \mathbb{R}\) are continuous.
For the entire collection see [Zbl 0838.00012].

MSC:

39A12 Discrete version of topics in analysis
39A10 Additive difference equations
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