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Boundedness in functional dynamic equations on time scales

Advances in Difference Equations volume 2006, Article number: 079689 (2006) Cite this article

Abstract

Using nonnegative definite Lyapunov functionals, we prove general theorems for the boundedness of all solutions of a functional dynamic equation on time scales. We apply our obtained results to linear and nonlinear Volterra integro-dynamic equations on time scales by displaying suitable Lyapunov functionals.

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Author information

Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Missouri-Rolla, 310 Rolla Building, Rolla, MO, 65409-0020, USA

    Elvan Akin-Bohner

  2. Department of Mathematics, University of Dayton, Dayton, OH, 45469-2316, USA

    Youssef N Raffoul

Authors
  1. Elvan Akin-Bohner
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  2. Youssef N Raffoul
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Corresponding author

Correspondence to Elvan Akin-Bohner.

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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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Akin-Bohner, E., Raffoul, Y.N. Boundedness in functional dynamic equations on time scales. Adv Differ Equ 2006, 079689 (2006). https://doi.org/10.1155/ADE/2006/79689

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  • DOI: https://doi.org/10.1155/ADE/2006/79689

Keywords

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