## Uniqueness implies existence and uniqueness criterion for nonlocal boundary value problems for third order differential equations

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- by Stephen Clark and Johnny Henderson PDF
- Proc. Amer. Math. Soc.
**134**(2006), 3363-3372 Request permission

## Abstract:

For the third order differential equation, $y''’ = f(x,y,y’,y''),$ we consider uniqueness implies existence results for solutions satisfying the nonlocal $4$-point boundary conditions, $y(x_1) = y_1,$ $y(x_2) = y_2,$ $y(x_3) - y(x_4) = y_3.$ Uniqueness of solutions of such boundary value problems is intimately related to solutions of the third order equation satisfying certain nonlocal $3$-point boundary conditions. These relationships are investigated as well.## References

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## Additional Information

**Stephen Clark**- Affiliation: Department of Mathematics, Baylor University, Waco, Texas 76798-7328
- Address at time of publication: Department of Mathematics and Statistics, University of Missouri-Rolla, Rolla, Missouri 65409
- Email: sclark@umr.edu
**Johnny Henderson**- Affiliation: Department of Mathematics, Baylor University Waco, Texas 76798-7328
- MR Author ID: 84195
- ORCID: 0000-0001-7288-5168
- Email: Johnny\underlineHenderson@baylor.edu
- Received by editor(s): February 18, 2005
- Received by editor(s) in revised form: May 20, 2005, and June 11, 2005
- Published electronically: May 18, 2006
- Additional Notes: Research for the first author was partially supported by NSF Grant DMS-0405528, as well as by a Baylor University Visiting Professorship during the Fall of 2004.
- Communicated by: Carmen C. Chicone
- © Copyright 2006
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc.
**134**(2006), 3363-3372 - MSC (2000): Primary 34B15; Secondary 34B10
- DOI: https://doi.org/10.1090/S0002-9939-06-08368-7
- MathSciNet review: 2231921