Advances in Difference Equations 
Volume 2004 (2004), Issue 3, Pages 201-210
doi:10.1155/S1687183904310083

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

Abstract

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.