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

Author(s): Stephen Clark; Johnny Henderson
Journal: Proc. Amer. Math. Soc. 134 (2006), 3363-3372.
MSC (2000): Primary 34B15; Secondary 34B10
Posted: May 18, 2006
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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: 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
Posted: 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 of article: Copyright 2006, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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