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

Advances in Difference Equations volume 2006, Article number: 031430 (2006) Cite this article

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.

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Authors and Affiliations

  1. Division of Mathematics, University of Dundee, Dundee DD1 4HN, Scotland, United Kingdom

    Fordyce A Davidson

  2. Department of Mathematics, Heriot-Watt University, Edinburgh, EH14 4AS, Scotland, United Kingdom

    Bryan P Rynne

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  1. Fordyce A Davidson
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  2. Bryan P Rynne
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Correspondence to Fordyce A Davidson.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Davidson, F.A., Rynne, B.P. The formulation of second-order boundary value problems on time scales. Adv Differ Equ 2006, 031430 (2006). https://doi.org/10.1155/ADE/2006/31430

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  • DOI: https://doi.org/10.1155/ADE/2006/31430

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