Advances in Difference Equations
Volume 2006 (2006), Article ID 31430, 10 pages
doi:10.1155/ADE/2006/31430

The formulation of second-order boundary value problems on time scales

Fordyce A. Davidson1 and Bryan P. Rynne2

1Division of Mathematics, University of Dundee, Dundee DD1 4HN, Scotland, United Kingdom
2Department of Mathematics, Heriot-Watt University, Edinburgh EH14 4AS, Scotland, United Kingdom

Received 6 February 2006; Revised 21 April 2006; Accepted 15 May 2006

Copyright © 2006 Fordyce A. Davidson and Bryan P. Rynne. 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

We reconsider the basic formulation of second-order, two-point, Sturm-Liouville-type boundary value problems on time scales. Although this topic has received extensive attention in recent years, we present some simple examples which show that there are certain difficulties with the formulation of the problem as usually used in the literature. These difficulties can be avoided by some additional conditions on the structure of the time scale, but we show that these conditions are unnecessary, since in fact, a simple, amended formulation of the problem avoids the difficulties.