Open Access

On lower and upper solutions without ordering on time scales

Advances in Difference Equations20062006:073860

DOI: 10.1155/ADE/2006/73860

Received: 31 January 2006

Accepted: 16 May 2006

Published: 13 September 2006

Abstract

In order to enlarge the set of boundary value problems on time scales, for which we can use the lower and upper solutions technique to get existence of solutions, we extend this method to the case when the pair lacks ordering. We use the degree theory and a priori estimates to obtain the existence of solutions for the second-order Dirichlet boundary value problems. To illustrate a wider application of this result, we conclude with an example which shows that a combination of well and non-well ordered pairs can yield the existence of multiple solutions.

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Authors’ Affiliations

(1)
Department of Mathematics, University of West Bohemia

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Copyright

© Petr Stehlík 2006

This article is published under license to BioMed Central Ltd. 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.