Asymptotic behaviour of solutions of nonlinear delay difference equations in Banach spaces

Asymptotic behaviour of solutions of nonlinear delay difference equations in Banach spaces

We consider the second-order nonlinear difference equations of the form Δ(rn−1Δxn−1)+pnf(xn−k)=hn. We show that there exists a solution (xn), which possesses the asymptotic behaviour ‖xn−a∑j=0n−1(1/rj)+b‖=o(1), a,b∈ℝ. In this paper, we extend the results of Agarwal (1992), Dawidowski et al. (2001),...

Full description

Bibliographic Details
Main Authors: Anna Kisiolek, Ireneusz Kubiaczyk
Format: Article
Language:English
Published: Hindawi Limited 2005-01-01
Series:International Journal of Mathematics and Mathematical Sciences
Online Access:http://dx.doi.org/10.1155/IJMMS.2005.2769
id doaj-d430b300755440a68b0b9cab47ca5598
record_format Article
spelling doaj-d430b300755440a68b0b9cab47ca55982020-11-24T21:18:29ZengHindawi LimitedInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252005-01-012005172769277410.1155/IJMMS.2005.2769Asymptotic behaviour of solutions of nonlinear delay difference equations in Banach spacesAnna Kisiolek0Ireneusz Kubiaczyk1Institute of Mathematics, Poznan University of Technology, 5 Maria Sklodowska-Curie Square, Poznan 60-965, PolandCollegium Mathematicum, Adam Mickiewicz University, Umultowska 87, Poznan 61-614, PolandWe consider the second-order nonlinear difference equations of the form Δ(rn−1Δxn−1)+pnf(xn−k)=hn. We show that there exists a solution (xn), which possesses the asymptotic behaviour ‖xn−a∑j=0n−1(1/rj)+b‖=o(1), a,b∈ℝ. In this paper, we extend the results of Agarwal (1992), Dawidowski et al. (2001), Drozdowicz and Popenda (1987), M. Migda (2001), and M. Migda and J. Migda (1988). We suppose that f has values in Banach space and satisfies some conditions with respect to the measure of noncompactness and measure of weak noncompactness.http://dx.doi.org/10.1155/IJMMS.2005.2769
collection DOAJ
language English
format Article
sources DOAJ
author Anna Kisiolek
Ireneusz Kubiaczyk
spellingShingle Anna Kisiolek
Ireneusz Kubiaczyk
Asymptotic behaviour of solutions of nonlinear delay difference equations in Banach spaces
International Journal of Mathematics and Mathematical Sciences
author_facet Anna Kisiolek
Ireneusz Kubiaczyk
author_sort Anna Kisiolek
title Asymptotic behaviour of solutions of nonlinear delay difference equations in Banach spaces
title_short Asymptotic behaviour of solutions of nonlinear delay difference equations in Banach spaces
title_full Asymptotic behaviour of solutions of nonlinear delay difference equations in Banach spaces
title_fullStr Asymptotic behaviour of solutions of nonlinear delay difference equations in Banach spaces
title_full_unstemmed Asymptotic behaviour of solutions of nonlinear delay difference equations in Banach spaces
title_sort asymptotic behaviour of solutions of nonlinear delay difference equations in banach spaces
publisher Hindawi Limited
series International Journal of Mathematics and Mathematical Sciences
issn 0161-1712
1687-0425
publishDate 2005-01-01
description We consider the second-order nonlinear difference equations of the form Δ(rn−1Δxn−1)+pnf(xn−k)=hn. We show that there exists a solution (xn), which possesses the asymptotic behaviour ‖xn−a∑j=0n−1(1/rj)+b‖=o(1), a,b∈ℝ. In this paper, we extend the results of Agarwal (1992), Dawidowski et al. (2001), Drozdowicz and Popenda (1987), M. Migda (2001), and M. Migda and J. Migda (1988). We suppose that f has values in Banach space and satisfies some conditions with respect to the measure of noncompactness and measure of weak noncompactness.
url http://dx.doi.org/10.1155/IJMMS.2005.2769
work_keys_str_mv AT annakisiolek asymptoticbehaviourofsolutionsofnonlineardelaydifferenceequationsinbanachspaces
AT ireneuszkubiaczyk asymptoticbehaviourofsolutionsofnonlineardelaydifferenceequationsinbanachspaces
_version_ 1726008904274411520

Similar Items