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Relationship Between Bounded Solutions of Differential Equations and Dynamic Equations on Time Scales

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A system of differential equations of the form \(\frac{dx}{dt}=X\left(t,x\right)\) and the corresponding system of dynamic equations with delta-derivative are considered. We establish conditions for the existence of bounded solutions to the system of dynamic equations on the time scale \({\mathbb{T}}_{\lambda }\) under the condition of existence of bounded solutions of the original system of differential equations. We obtain conditions for the graininess function under which the existence of bounded solutions of differential equations implies the existence of solutions of the corresponding system of dynamic equations.

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Authors and Affiliations

  1. T. Shevchenko National University of Kyiv, Academician Hlushkov Ave., 4E, Kyiv, 03022, Ukraine

    Viktoriia Tsan & Yuriy Perestyuk

  2. “I. Sikorsky Kyiv Polytechnic Institute” Ukrainian National Technical University, Peremoha Ave., 37, Kyiv, 03056, Ukraine

    Viktoriia Mogylova

Authors
  1. Viktoriia Tsan
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  2. Yuriy Perestyuk
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  3. Viktoriia Mogylova
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Correspondence to Viktoriia Tsan.

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Translated from Neliniini Kolyvannya, Vol. 26, No. 2, pp. 274–293, April–June, 2023. Ukrainian DOI: https://doi.org/10.37863/nosc.v26i2.1433.

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Tsan, V., Perestyuk, Y. & Mogylova, V. Relationship Between Bounded Solutions of Differential Equations and Dynamic Equations on Time Scales. J Math Sci 279, 414–437 (2024). https://doi.org/10.1007/s10958-024-07022-2

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  • DOI: https://doi.org/10.1007/s10958-024-07022-2

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