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International Journal of Mathematics and Mathematical Sciences
Volume 2003, Issue 39, Pages 2455-2463
http://dx.doi.org/10.1155/S0161171203211509

A necessary and sufficient condition for the existence of a unique solution of a discrete boundary value problem

Raghib Abu-Saris1 and Wajdi Ahmad2

1Department of Basic Sciences, University of Sharjah, P.O. Box 27272, Sharjah, United Arab Emirates
2Department of Electrical and Electronics Engineering, University of Sharjah, P.O. Box 27272, Sharjah, United Arab Emirates

Received 4 November 2002; Revised 25 February 2003

Copyright © 2003 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

A kth-order linear difference equation with constant coefficients subject to boundary conditions is considered. A necessary and sufficient condition for the existence of a unique solution for such a boundary value problem is established. The condition established answers a fundamental question for well-posedness and can be easily applied using a simple and computationally tractable algorithm that does not require finding the roots of the associated characteristic equation.