Document Type
Article
Publication Date
6-14-2016
Publication Source
Electronic Journal of Qualitative Theory of Differential Equations
Abstract
We consider two simple boundary value problems at resonance for an ordinary differential equation. Employing a shift argument, a regular fixed point operator is constructed. We employ the monotone method coupled with a method of upper and lower solutions and obtain sufficient conditions for the existence of solutions of boundary value problems at resonance for nonlinear boundary value problems. Three applications are presented in which explicit upper solutions and lower solutions are exhibited for the first boundary value problem. Two applications are presented for the second boundary value problem. Of interest, the upper and lower solutions are easily and explicitly constructed. Of primary interest, the upper and lower solutions are elements of the kernel of the linear problem at resonance.
Inclusive pages
1-13
ISBN/ISSN
1417-3875
Document Version
Published Version
Copyright
Copyright © 2016, The Author(s)
Publisher
Bolyai Institute, University of Szeged and the Hungarian Academy of Sciences
Volume
40
Peer Reviewed
yes
eCommons Citation
Al Mosa, Samerah and Eloe, Paul W., "Upper and Lower Solution Method for Boundary Value Problems at Resonance" (2016). Mathematics Faculty Publications. 77.
https://ecommons.udayton.edu/mth_fac_pub/77
COinS
Comments
This document has been made available for download in accordance with the publisher's policy on open access.
DOI: https://doi.org/10.14232/ejqtde.2016.1.40
Permission documentation on file.