Positive solutions of nonlinear differential equations with prescribed decay of the first derivative
(2005) In Nonlinear Analysis: Theory, Methods & Applications 60(1). p.179-185- Abstract
- An existence and uniqueness result for bounded, positive solutions x(t) of the equation u" + f (t, u, u') = 0, t greater than or equal to t(0) greater than or equal to 0, is established by means of the Banach contraction principle. For such a solution it is shown that alpha(t) less than or equal to x'(t) less than or equal to beta(t), t greater than or equal to t(0), where alpha, beta are given nonnegative, continuous functions which are integrable over [t(0), +infinity). The result complements others known in the literature.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/259516
- author
- Mustafa, Octavian LU
- organization
- publishing date
- 2005
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- nonlinear differential equation, monotone positive solution, contraction principle, Banach
- in
- Nonlinear Analysis: Theory, Methods & Applications
- volume
- 60
- issue
- 1
- pages
- 179 - 185
- publisher
- Elsevier
- external identifiers
-
- wos:000225514100011
- scopus:9344256108
- ISSN
- 0362-546X
- DOI
- 10.1016/j.na.2004.08.032
- language
- English
- LU publication?
- yes
- id
- a1c406c3-43e4-46ff-84a5-d1560412d256 (old id 259516)
- date added to LUP
- 2016-04-01 16:39:02
- date last changed
- 2022-03-22 20:09:13
@article{a1c406c3-43e4-46ff-84a5-d1560412d256, abstract = {{An existence and uniqueness result for bounded, positive solutions x(t) of the equation u" + f (t, u, u') = 0, t greater than or equal to t(0) greater than or equal to 0, is established by means of the Banach contraction principle. For such a solution it is shown that alpha(t) less than or equal to x'(t) less than or equal to beta(t), t greater than or equal to t(0), where alpha, beta are given nonnegative, continuous functions which are integrable over [t(0), +infinity). The result complements others known in the literature.}}, author = {{Mustafa, Octavian}}, issn = {{0362-546X}}, keywords = {{nonlinear differential equation; monotone positive solution; contraction principle; Banach}}, language = {{eng}}, number = {{1}}, pages = {{179--185}}, publisher = {{Elsevier}}, series = {{Nonlinear Analysis: Theory, Methods & Applications}}, title = {{Positive solutions of nonlinear differential equations with prescribed decay of the first derivative}}, url = {{http://dx.doi.org/10.1016/j.na.2004.08.032}}, doi = {{10.1016/j.na.2004.08.032}}, volume = {{60}}, year = {{2005}}, }