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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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