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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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


Authors: Stephen Clark and Johnny Henderson
Journal: Proc. Amer. Math. Soc. 134 (2006), 3363-3372
MSC (2000): Primary 34B15; Secondary 34B10
Published electronically: May 18, 2006
MathSciNet review: 2231921
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Abstract | References | Similar Articles | Additional Information

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.


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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
Email: Johnny\underlineHenderson@baylor.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-06-08368-7
PII: S 0002-9939(06)08368-7
Keywords: Boundary value problem, uniqueness, existence, nonlocal
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
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.