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On lower and upper solutions without ordering on time scales

Advances in Difference Equations volume 2006, Article number: 073860 (2006) Cite this article

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 and Affiliations

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

    Petr Stehlík

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  1. Petr Stehlík
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Correspondence to Petr Stehlík.

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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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Stehlík, P. On lower and upper solutions without ordering on time scales. Adv Differ Equ 2006, 073860 (2006). https://doi.org/10.1155/ADE/2006/73860

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  • DOI: https://doi.org/10.1155/ADE/2006/73860

Keywords

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