Bounded solutions and asymptotic stability to nonlinear second-order neutral difference equations with quasi-differences

This work is devoted to the study of the nonlinear second-order neutral difference equations with quasi-differences of the form $$ \Delta \left( r_{n} \Delta \left( x_{n}+q_{n}x_{n-\tau}\right)\right)= a_{n}f(x_{n-\sigma})+b_n%, \ n\geq n_0 $$ with respect to \((q_n)\). For \(q_n\to1\), \(q_n\in(0,1...

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Bibliographic Details
Published in:arXiv.org 2016-07
Main Author: Nockowska-Rosiak, Magdalena
Format: Article
Language:English
Subjects:
Difference equations
Existence theorems
Fixed points (mathematics)
Mathematical analysis
Nonlinear equations
Online Access:Get full text
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Summary:This work is devoted to the study of the nonlinear second-order neutral difference equations with quasi-differences of the form $$ \Delta \left( r_{n} \Delta \left( x_{n}+q_{n}x_{n-\tau}\right)\right)= a_{n}f(x_{n-\sigma})+b_n%, \ n\geq n_0 $$ with respect to \((q_n)\). For \(q_n\to1\), \(q_n\in(0,1)\) the standard fixed point approach is not sufficed to get the existence of the bounded solution, so we combine this method with an approximation technique to achieve our goal. Moreover, for \(p\ge 1\) and \(\sup|q_n|
ISSN:2331-8422