On the existence of solutions with prescribed asymptotic behaviour for perturbed nonlinear differential equations of second order
(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:
https://lup.lub.lu.se/record/406818
- author
- Mustafa, Octavian LU
- organization
- publishing date
- 2005
- 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}}, }