# Asymptotic integration of second-order nonlinear difference equations

 dc.identifier.uri http://dx.doi.org/10.15488/2661 dc.identifier.uri http://www.repo.uni-hannover.de/handle/123456789/2687 dc.contributor.author Ehrnström, Mats dc.contributor.author Tisdell, Christopher C. dc.contributor.author Wahlén, Erik dc.date.accessioned 2018-01-29T10:20:25Z dc.date.available 2018-01-29T10:20:25Z dc.date.issued 2011 dc.identifier.citation Ehrnström, M.; Tisdell, C.C.; Wahlén, E.: Asymptotic integration of second-order nonlinear difference equations. In: Glasgow Mathematical Journal 53 (2011), Nr. 2, S. 223-243. DOI: https://doi.org/10.1017/S0017089510000650 dc.description.abstract In this work we analyse a nonlinear, second-order difference equation on an unbounded interval. We present new conditions under which the problem admits a unique solution that is of a particular linear asymptotic form. The results concern the general behaviour of solutions to the initial-value problem, as well as solutions with a given asymptote. Our methods involve establishing suitable complete metric spaces and an application of Banach's fixed-point theorem. For the solutions found in our two main theorems fixed initial data and fixed asymptote, respectively we establish exact convergence rates to solutions of the differential equation related to our difference equation. It turns out that for the asymptotic case there is uniform convergence for both the solution and its derivative, while in the other case the convergence is somewhat weaker. Two different techniques are utilized, and for each one has to employ ad-hoc methods for the unbounded interval. Of particular importance is the exact form of the operators and metric spaces formulated in the earlier sections. © 2011 Glasgow Mathematical Journal Trust. eng dc.language.iso eng dc.publisher Cambridge : Cambridge University Press dc.relation.ispartofseries Glasgow Mathematical Journal 53 (2011), Nr. 2 dc.rights Es gilt deutsches Urheberrecht. Das Dokument darf zum eigenen Gebrauch kostenfrei genutzt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden. Dieser Beitrag ist aufgrund einer (DFG-geförderten) Allianz- bzw. Nationallizenz frei zugänglich. dc.subject second-order difference equation eng dc.subject Banach’s fixed-point theorem eng dc.subject.ddc 510 | Mathematik ger dc.title Asymptotic integration of second-order nonlinear difference equations dc.type article dc.type Text dc.relation.issn 0017-0895 dc.relation.doi https://doi.org/10.1017/S0017089510000650 dc.bibliographicCitation.issue 2 dc.bibliographicCitation.volume 53 dc.bibliographicCitation.firstPage 223 dc.bibliographicCitation.lastPage 243 dc.description.version publishedVersion tib.accessRights frei zug�nglich
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