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Title: Linearized Oscillation of Nonlinear Difference Equations with Advanced Arguments (English)
Author: Öcalan, Özkan
Language: English
Journal: Archivum Mathematicum
ISSN: 0044-8753 (print)
ISSN: 1212-5059 (online)
Volume: 45
Issue: 3
Year: 2009
Pages: 203-212
Summary lang: English
Category: math
Summary: This paper is concerned with the nonlinear advanced difference equation with constant coefficients \[ x_{n+1}-x_{n}+\sum _{i=1}^{m}p_{i}f_{i}(x_{n-k_{i}})=0\,,\quad n=0,1,\dots \] where $p_{i}\in (-\infty ,0)$ and $k_{i}\in \lbrace \dots ,-2,-1\rbrace $ for $i=1,2,\dots ,m$. We obtain sufficient conditions and also necessary and sufficient conditions for the oscillation of all solutions of the difference equation above by comparing with the associated linearized difference equation. Furthermore, oscillation criteria are established for the nonlinear advanced difference equation with variable coefficients \[ x_{n+1}-x_{n}+\sum _{i=1}^{m}p_{in}f_{i}(x_{n-k_{i}})=0\,,\quad n=0,1,\dots \] where $p_{in}\le 0$ and $k_{i}\in \lbrace \dots ,-2,-1\rbrace $ for $i=1,2,\dots , m$. (English)
Keyword: advanced difference equation
Keyword: delay difference equation
Keyword: nonlinear
Keyword: oscillation
MSC: 34K11
MSC: 39A10
MSC: 39A12
MSC: 39A21
idZBL: Zbl 1212.39005
idMR: MR2591676
Date available: 2009-09-18T11:25:30Z
Last updated: 2013-09-19
Stable URL:
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