Advances in Difference Equations
Volume 2004 (2004), Issue 3, Pages 201-210

Maximum principles for a family of nonlocal boundary value problems

Paul W. Eloe

Department of Mathematics, University of Dayton, Dayton 45469-2316, OH, USA

Received 21 October 2003; Revised 16 February 2004

Copyright © 2004 Paul W. Eloe. 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.


We study a family of three-point nonlocal boundary value problems (BVPs) for an nth-order linear forward difference equation. In particular, we obtain a maximum principle and determine sign properties of a corresponding Green function. Of interest, we show that the methods used for two-point disconjugacy or right-disfocality results apply to this family of three-point BVPs.