Two-point boundary value problems for ordinary differential equations, uniqueness implies existence
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- by Paul W. Eloe and Johnny Henderson
- Proc. Amer. Math. Soc. 148 (2020), 4377-4387
- DOI: https://doi.org/10.1090/proc/15115
- Published electronically: July 20, 2020
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Corrigendum: Proc. Amer. Math. Soc. 150 (2022), 3649-3654.
Abstract:
We consider a family of two-point $n-1 ,1$ boundary value problems for $n$th order nonlinear ordinary differential equations and obtain conditions in terms of uniqueness of solutions that 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 shall replace that standard hypothesis with one in which we assume uniqueness of solutions of a large family of two-point boundary value problems. We then obtain readily verifiable conditions on the nonlinear term that in fact imply the uniqueness of solutions of the large family of two-point boundary value problems.References
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Bibliographic Information
- Paul W. Eloe
- Affiliation: Department of Mathematics, University of Dayton, Dayton, Ohio 45469
- MR Author ID: 63110
- ORCID: 0000-0002-6590-9931
- Email: peloe1@udayton.edu
- Johnny Henderson
- Affiliation: Department of Mathematics, Baylor University, Waco, Texas 76798
- MR Author ID: 84195
- ORCID: 0000-0001-7288-5168
- Email: Johnny_Henderson@baylor.edu
- Received by editor(s): February 20, 2020
- Published electronically: July 20, 2020
- Communicated by: Wenxian Shen
- © Copyright 2020 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 148 (2020), 4377-4387
- MSC (2010): Primary 34B15; Secondary 34B10
- DOI: https://doi.org/10.1090/proc/15115
- MathSciNet review: 4135304