Oscillation of two-dimensional difference systems
type: Item
instance of: scholarly article
title: Oscillation of two-dimensional difference systems
zbMATH Open document ID: 0964.39012
DOI: 10.1016/S0898-1221(99)00246-1
author: John R. Graef
author: E. Thandapani
publication date: 2001-07-11T00:00:00Z
review text: The paper presents some oscillation results for the two-dimensional difference system \[ \begin{aligned} \triangle x_n&=b_ng(y_n),\\ \triangle y_{n-1}&=-a_nf(x_n), \end{aligned} \qquad n\in\mathbb N (n_0)=\{n_0,n_0+1,\dots \}, \tag{1} \] where \(n_0\in\mathbb N\), \(\{a_n\}, \{b_n\}\), \(n\in\mathbb N (n_0)\) are real sequences and \(f, g\) are real continuous functions with the sign property \(uf(u)>0\) and \(ug(u)>0\) for all \(u\neq 0\). Assuming both sequences \(\{a_n\}, \{b_n\}\) are nonnegative and not identically zero for infinitely many values of \(n\) the authors establish the sufficient conditions for all solutions to the system (1) to be oscillatory. Moreover, some of their results do not require the sign condition on \(\{a_n\}\), i.e., \(\{a_n\}\) can assume both positive and negative values. The difference system (1) can be reduced via a special choice of \(f, g\) and \(b_n\) to the second order superlinear or sublinear equation. It is shown that the derived oscillation results generalize the known oscillation criteria for this type of difference equations.
reviewed by: Jan Čermák
Mathematics Subject Classification ID: 39A11
zbMATH DE Number: 1429540
zbMATH Keywords: nonlinear difference system
zbMATH Keywords: oscillation
MaRDI profile type: Publication
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published in: Computers & Mathematics with Applications
description: scientific article; zbMATH DE number 1429540