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Boundary-Value Problems for Third-Order Lipschitz Ordinary Differential Equations

Part of: Boundary value problems

Published online by Cambridge University Press:  28 October 2014

John R. Graef ,
Johnny Henderson ,
Rodrica Luca  and
Yu Tian
John R. Graef
Affiliation:
Department of Mathematics, University of Tennesseeat Chattanooga, Chattanooga, TN 37403-2598, USA, (john-graef@utc.edu)
Johnny Henderson
Affiliation:
Department of Mathematics, Baylor UniversityWaco, TX 76798-7328, USA, (johnny_henderson@baylor.edu)
Rodrica Luca
Affiliation:
Department of Mathematics, Gheorghe Asachi Technical University, Iasi 700506, Romania, (rluca@math.tuiasi.ro)
Yu Tian
Affiliation:
School of Science, Beijing University of Posts and Telecommunications, Beijing 100876, People's Republic of China (, tianyu2992@163.com)
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Abstract

For the third-order differential equation y′″ = ƒ(t, y, y′, y″), where , questions involving ‘uniqueness implies uniqueness’, ‘uniqueness implies existence’ and ‘optimal length subintervals of (a, b) on which solutions are unique’ are studied for a class of two-point boundary-value problems.

Keywords

boundary-value problemLipschitz equationuniquenessexistencePontryagin maximum principleoptimal length interval

MSC classification

Primary: 34B15: Nonlinear boundary value problems
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 58 , Issue 1 , February 2015 , pp. 183 - 197
Copyright
Copyright © Edinburgh Mathematical Society 2015 

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