Remarks on oscillation of second-order linear difference equation
type: Item
instance of: scholarly article
title: Remarks on oscillation of second-order linear difference equation
zbMATH Open document ID: 1197.39003
author: Caiming Lei
published in: Applied Mathematics and Computation
publication date: 2010-01-08T00:00:00Z
review text: The research on difference equations in the real domain is developed and many interesting results were obtained. In this paper the author considers the second order linear difference equation \[ \Delta^2 x_{n-1}+p_n x_n =0,\quad n=1,2,\dots, \] where \(\Delta\) is the forward difference operator \(\Delta x_n =x_{n+1}-x_n\), and \(\{p_n\}\) is a sequence of nonnegative real numbers. He considers existence conditions for oscillating solutions of the above difference equation, which are based on incorrect conditions, an incorrect proof and an incorrect result.
reviewed by: Zhibo Huang
Mathematics Subject Classification ID: 39A21
Mathematics Subject Classification ID: 39A10
Mathematics Subject Classification ID: 39A06
zbMATH DE Number: 5655274
zbMATH Keywords: difference equations
zbMATH Keywords: nonoscillatory
zbMATH Keywords: oscillatory
zbMATH Keywords: second-order linear difference equation
MaRDI profile type: Publication
full work available at URL: j.amc.2009.09.028
OpenAlex ID: W2064737778
cites work: Q3989353
cites work: Q4849090
cites work: Q3034267
cites work: Oscillation and nonoscillation for second-order linear difference equations
cites work: Oscillations of delay difference equations in a critical state
cites work: Oscillation criteria for second-order linear difference equations.
DOI: 10.1016/J.AMC.2009.09.028
description: scientific article; zbMATH DE number 5655274