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On the existence of solutions with prescribed asymptotic behaviour for perturbed nonlinear differential equations of second order

Mustafa, Octavian LU (2005) In Glasgow Mathematical Journal 47. p.177-185
Abstract
A global existence result for solutions u(t) of the differential equation x" + f(t, x) = p(t), t >= t(0) >= 1, that can be written as u(t) = P(t) + o(l) for all large t, where P"(t) = p(t), is established by means of the Schauder-Tikhonov theorem. It generalizes the recent work of Lipovan [On the asymptotic behaviour of the solutions to a class of second order nonlinear differential equations, Glasgow Math. J. 45 (2003), 179-187] and allows for a unifying treatment of the existence problems concerning asymptotically linear and oscillatory solutions of second order nonlinear differential equations.
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
Glasgow Mathematical Journal
volume
47
pages
177 - 185
publisher
Cambridge University Press
external identifiers
  • wos:000238197100014
  • scopus:13744250880
ISSN
0017-0895
DOI
10.1017/S0017089504002228
language
English
LU publication?
yes
id
ab1d1b98-6870-40b1-a817-911154cab48d (old id 406818)
date added to LUP
2016-04-01 11:48:48
date last changed
2022-04-05 05:28:21
@article{ab1d1b98-6870-40b1-a817-911154cab48d,
  abstract     = {{A global existence result for solutions u(t) of the differential equation x" + f(t, x) = p(t), t >= t(0) >= 1, that can be written as u(t) = P(t) + o(l) for all large t, where P"(t) = p(t), is established by means of the Schauder-Tikhonov theorem. It generalizes the recent work of Lipovan [On the asymptotic behaviour of the solutions to a class of second order nonlinear differential equations, Glasgow Math. J. 45 (2003), 179-187] and allows for a unifying treatment of the existence problems concerning asymptotically linear and oscillatory solutions of second order nonlinear differential equations.}},
  author       = {{Mustafa, Octavian}},
  issn         = {{0017-0895}},
  language     = {{eng}},
  pages        = {{177--185}},
  publisher    = {{Cambridge University Press}},
  series       = {{Glasgow Mathematical Journal}},
  title        = {{On the existence of solutions with prescribed asymptotic behaviour for perturbed nonlinear differential equations of second order}},
  url          = {{http://dx.doi.org/10.1017/S0017089504002228}},
  doi          = {{10.1017/S0017089504002228}},
  volume       = {{47}},
  year         = {{2005}},
}