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
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.