Positive solutions of nonlinear differential equations with prescribed decay of the first derivative
(2005) In Nonlinear Analysis: Theory, Methods & Applications 60(1). p.179185 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:
http://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
 0362546X
 DOI
 10.1016/j.na.2004.08.032
 language
 English
 LU publication?
 yes
 id
 a1c406c343e446ff84a5d1560412d256 (old id 259516)
 date added to LUP
 20070822 13:22:56
 date last changed
 20180107 09:26:02
@article{a1c406c343e446ff84a5d1560412d256, 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 = {0362546X}, keyword = {nonlinear differential equation,monotone positive solution,contraction principle,Banach}, language = {eng}, number = {1}, pages = {179185}, 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}, }