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  • Research Article
  • Open Access

On lower and upper solutions without ordering on time scales

Advances in Difference Equations20062006:073860

  • Received: 31 January 2006
  • Accepted: 16 May 2006
  • Published:


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.


  • Differential Equation
  • Partial Differential Equation
  • Ordinary Differential Equation
  • Functional Analysis
  • Functional Equation


Authors’ Affiliations

Department of Mathematics, University of West Bohemia, Univerzitní 22, Plzeň 306 14, Czech Republic


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© 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.