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

DOI:
https://doi.org/10.1090/S0002-9939-06-08368-7

Published electronically:
May 18, 2006

MathSciNet review:
2231921

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: For the third order differential equation, we consider uniqueness implies existence results for solutions satisfying the nonlocal -point boundary conditions, Uniqueness of solutions of such boundary value problems is intimately related to solutions of the third order equation satisfying certain nonlocal -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:
https://doi.org/10.1090/S0002-9939-06-08368-7

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.