文章基本信息

标题：Existence and iterative approximations of nonoscillatory solutions for second order nonlinear neutral delay difference equations
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作者：Guojing Jiang ; Liangshi Zhao ; Shin Min Kang 等
期刊名称：Advances in Difference Equations
印刷版ISSN：1687-1839
电子版ISSN：1687-1847
出版年度：2015
卷号：2015
期号：1
页码：368
DOI：10.1186/s13662-015-0702-5
语种：English
出版社：Hindawi Publishing Corporation
摘要：This paper investigates the second order nonlinear neutral delay difference equation Δ [ a n Δ ( x n + b x n − τ − d n ) ] + Δ f ( n , x f 1 ( n ) , x f 2 ( n ) , … , x f k ( n ) ) + g ( n , x g 1 ( n ) , x g 2 ( n ) , … , x g k ( n ) ) = c n , n ≥ n 0 . $$\begin{aligned}& \Delta \bigl[a_{n}\Delta (x_{n}+bx_{n-\tau}-d_{n} ) \bigr] +\Delta f (n,x_{f_)(n)},x_{f_,(n)},\ldots,x_{f_{k}(n)} ) \\& \quad{} +g (n,x_{g_)(n)},x_{g_,(n)},\ldots,x_{g_{k}(n)} )=c_{n},\quad n\ge n_(. \end{aligned}$$ By using the Banach fixed point theorem and some new techniques, we establish the existence results of uncountably many bounded nonoscillatory solutions for the above equation, propose a few Mann type iterative approximation schemes with errors and obtain several errors estimates between the iterative approximations and the nonoscillatory solutions. Examples that cannot be solved by known results are given to illustrate our theorems.
关键词：Second order nonlinear neutral delay difference equation ; uncountably many bounded nonoscillatory solutions ; Banach fixed point theorem ; Mann iterative sequence with errors