Skip Navigation



IMA Journal of Applied Mathematics Advance Access published online on February 16, 2008
IMA Journal of Applied Mathematics, doi:10.1093/imamat/hxn001
This Article
Right arrow Full Text (PDF)
Right arrow All Versions of this Article:
73/2/323    most recent
hxn001v1
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
Right arrowRequest Permissions
Google Scholar
Right arrow Articles by O'Regan, D.
Right arrow Articles by El-Gebeily, M.
Right arrow Search for Related Content
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

© The Author 2008. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Existence, upper and lower solutions and quasilinearization for singular differential equations

Donal O'Regan

Department of Mathematical Sciences, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia

Mohamed El-Gebeily{dagger}

Department of Mathematics, National University of Ireland, Galway, Ireland

{dagger} Email: mgebeily{at}kfupm.edu.sa

Received on July 12, 2005; Revision received December 7, 2007. In this paper, we discuss existence theorems in the presence of upper and lower solutions as well as the method of quasilinearization (QSL) for general non-linear second-order singular ordinary differential equations. We show the existence of solutions under the assumption of weak continuity of the non-linear part. If the non-linear part is monotone decreasing, a solution may be obtained by the QSL method as the strong limit of a quadratically convergent sequence of approximate solutions. Under stronger assumptions on the linear and the non-linear parts, a solution is quadratically bracketed between two monotone sequences of approximate solutions of certain related linear equations.

Keywords: singular differential equations; self-adjoint operators; non-linear operators; upper and lower solutions; existence; quasilinearization methods.


Add to CiteULike CiteULike   Add to Connotea Connotea   Add to Del.icio.us Del.icio.us    What's this?




Disclaimer:
Please note that abstracts for content published before 1996 were created through digital scanning and may therefore not exactly replicate the text of the original print issues. All efforts have been made to ensure accuracy, but the Publisher will not be held responsible for any remaining inaccuracies. If you require any further clarification, please contact our Customer Services Department.