On existence of positive solutions and bounded oscillations for neutral difference equations
type: Item
instance of: scholarly article
title: On existence of positive solutions and bounded oscillations for neutral difference equations
zbMATH Open document ID: 0763.39002
DOI: 10.1016/0022-247X(92)90342-B
published in: Journal of Mathematical Analysis and Applications
publication date: 1992-09-27T00:00:00Z
review text: The authors consider the linear homogeneous difference equation \(\Delta^ \alpha(x_ n-cx_{n-m})+p_ n x_{n-k}=0\), where \(c,p_ n\geq 0\). Here \(\Delta\) is the forward difference operator, \(\Delta x_ n=x_{n+1}-x_ n\), and \(\alpha=1,2\). It is shown that positive solutions tending to zero or \(\infty\) or remaining bounded, or oscillatory solutions, respectively, exist under appropriate conditions on \(c\) and \(p_ n\). Reviewer's remark: The right-hand sides of equations (2.17) and (2.20) should read \((n+3)/(n^ 2(n+1))\) and \((n+3)/(n(n+1))\), respectively, for these equations to have the indicated solutions.
Mathematics Subject Classification ID: 39A10
zbMATH DE Number: 62811
zbMATH Keywords: bounded solutions
zbMATH Keywords: linear homogeneous difference equation
zbMATH Keywords: positive solutions
zbMATH Keywords: oscillatory solutions
author: Bikkar S. Lalli
author: B. G. Zhang
reviewed by: Rémi Vaillancourt
MaRDI profile type: Publication
cites work: On the numerical integration of a symmetric system of difference- differential equations of neutral type
cites work: Oscillation of discrete analogues of delay equations
cites work: Oscillations of neutral difference equations
cites work: Linearized oscillations for equations with piecewise constant arguments
cites work: Explicit conditions for the oscillation of difference equations
cites work: Q3356799
cites work: Q3031394
cites work: Sharp conditions for the oscillation of delay difference equations
cites work: On the oscillation of solutions and existence of positive solutions of neutral difference equations
cites work: Q3694040
cites work: Q3721093
description: scientific article; zbMATH DE number 62811