文章基本信息

标题：Asymptotically polynomial solutions of difference equations
本地全文：下载
作者：Janusz Migda
期刊名称：Advances in Difference Equations
印刷版ISSN：1687-1839
电子版ISSN：1687-1847
出版年度：2013
卷号：2013
期号：1
页码：92
DOI：10.1186/1687-1847-2013-92
语种：English
出版社：Hindawi Publishing Corporation
摘要：Asymptotic properties of solutions of a difference equation of the form Δ m x n = a n f ( n , x σ ( n ) ) + b n are studied. We present sufficient conditions under which, for any polynomial φ ( n ) of degree at most m − 1 and for any real s ≤ 0 , there exists a solution x of the above equation such that x n = φ ( n ) + o ( n s ) . We give also sufficient conditions under which, for given real s ≤ m − 1 , all solutions x of the equation satisfy the condition x n = φ ( n ) + o ( n s ) for some polynomial φ ( n ) of degree at most m − 1 . MSC:39A10.
关键词：difference equation ; asymptotically polynomial solution ; prescribed asymptotic behavior