Oscillation criteria for certain difference equations with continuous variables
type: Item
instance of: scholarly article
title: Oscillation criteria for certain difference equations with continuous variables
zbMATH Open document ID: 1123.39011
author: Fu Yun Lian
author: B. G. Zhang
published in: Indian Journal of Pure \& Applied Mathematics
publication date: 2007-05-11T00:00:00Z
review text: Consider the difference equation with continuous arguments \[ x(t)-x(t-\tau)+\sum_{i=1}^m p_i(t)x(t-\sigma_i)=0,\quad t\geq 0, \] where \(0 < \tau < \sigma_1 < \dots < \sigma_m\), \(p_i\in C (\mathbb R, \mathbb R_+)\), \(\lim\inf_{t\to\infty} p_i(t)=\bar p_i\), \(i=1,2,\dots,m\). The authors give sufficient conditions for the oscillation of all solutions of the above equation in the case when the corresponding limiting equation \[ x(t)-x(t-\tau)+\sum_{i=1}^m \bar p_i x(t-\sigma_i)=0,\quad t\geq 0, \] admits non-oscillatory solutions.
Mathematics Subject Classification ID: 39A11
zbMATH DE Number: 5151964
zbMATH Keywords: difference equation with continuous arguments
zbMATH Keywords: oscillation
reviewed by: B. G. Pachpatte
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 5151964