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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.
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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
2007-08-21 08:50:14
date last changed
2017-06-11 03:29:55
@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},
  volume       = {47},
  year         = {2005},
}