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Theory and Modern Applications

Boundedness in functional dynamic equations on time scales

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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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