Asymptotic Integration Of SecondOrder Nonlinear Difference Equations
(2011) In Glasgow Mathematical Journal 53. p.223243 Abstract
 In this work we analyse a nonlinear, secondorder 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 initialvalue problem, as well as solutions with a given asymptote. Our methods involve establishing suitable complete metric spaces and an application of Banach's fixedpoint theorem. For the solutions found in our two main theoremsfixed initial data and fixed asymptote, respectivelywe 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... (More)
 In this work we analyse a nonlinear, secondorder 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 initialvalue problem, as well as solutions with a given asymptote. Our methods involve establishing suitable complete metric spaces and an application of Banach's fixedpoint theorem. For the solutions found in our two main theoremsfixed initial data and fixed asymptote, respectivelywe 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 adhoc methods for the unbounded interval. Of particular importance is the exact form of the operators and metric spaces formulated in the earlier sections. (Less)
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/record/1925950
 author
 Ehrnstroem, Mats; Tisdell, Christopher C. and Wahlén, Erik ^{LU}
 organization
 publishing date
 2011
 type
 Contribution to journal
 publication status
 published
 subject
 in
 Glasgow Mathematical Journal
 volume
 53
 pages
 223  243
 publisher
 Cambridge University Press
 external identifiers

 wos:000288615900002
 scopus:82455175688
 ISSN
 00170895
 DOI
 10.1017/S0017089510000650
 language
 English
 LU publication?
 yes
 id
 de02ebc2f8a44eaa86f593f25e0c173c (old id 1925950)
 date added to LUP
 20110510 14:51:25
 date last changed
 20180107 04:05:52
@article{de02ebc2f8a44eaa86f593f25e0c173c, abstract = {In this work we analyse a nonlinear, secondorder 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 initialvalue problem, as well as solutions with a given asymptote. Our methods involve establishing suitable complete metric spaces and an application of Banach's fixedpoint theorem. For the solutions found in our two main theoremsfixed initial data and fixed asymptote, respectivelywe 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 adhoc methods for the unbounded interval. Of particular importance is the exact form of the operators and metric spaces formulated in the earlier sections.}, author = {Ehrnstroem, Mats and Tisdell, Christopher C. and Wahlén, Erik}, issn = {00170895}, language = {eng}, pages = {223243}, publisher = {Cambridge University Press}, series = {Glasgow Mathematical Journal}, title = {Asymptotic Integration Of SecondOrder Nonlinear Difference Equations}, url = {http://dx.doi.org/10.1017/S0017089510000650}, volume = {53}, year = {2011}, }