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Positive solutions of nonlinear differential equations with prescribed decay of the first derivative

Mustafa, Octavian LU (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.
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author
organization
publishing date
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
2007-08-22 13:22:56
date last changed
2017-07-30 04:39:33
@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},
  keyword      = {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},
  volume       = {60},
  year         = {2005},
}