Document Type
Article
Publication Date
2020
Publication Source
Electronic Journal of Qualitative Theory of Differential Equations
Abstract
We consider a family of three point n − 2, 1, 1 conjugate boundary value problems for nth order nonlinear ordinary differential equations and obtain conditions in terms of uniqueness of solutions imply existence of solutions. A standard hypothesis that has proved effective in uniqueness implies existence type results is to assume uniqueness of solutions of a large family of n−point boundary value problems. Here, we replace that standard hypothesis with one in which we assume uniqueness of solutions of large families of two and three point boundary value problems. We then close the paper with verifiable conditions on the nonlinear term that in fact imply global uniqueness of solutions of the large family of three point boundary value problems.
ISBN/ISSN
1417-3875
Document Version
Published Version
Volume
2020
Peer Reviewed
yes
Keywords
uniqueness implies existence, nonlinear interpolation, ordinary differential equations, three point boundary value problems
eCommons Citation
Eloe, Paul W.; Henderson, Johnny; and Neugebauer, Jeffrey T., "Three Point Boundary Value Problems for Ordinary Differential Equations, Uniqueness Implies Existence" (2020). Mathematics Faculty Publications. 216.
https://ecommons.udayton.edu/mth_fac_pub/216
Comments
The document is made available in compliance with the publisher's policy on self-archiving. Permission documentation is on file.
The Electronic Journal of Qualitative Theory of Differential Equations is an open access journal which means that all content is freely available without charge to the user or his/her institution. Users are allowed to read, download, copy, distribute, print, search, or link to the full texts of the articles, or use them for any other lawful purpose, without asking prior permission from the publisher or the author. This is in accordance with the BOAI definition of open access. There are no charges and fees for publication, either.
Paper is in Volume 2020, paper No. 74. DOI: https://doi.org/10.14232/ejqtde.2020.1.74