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Bounded Solutions of Difference Equations in a Banach Space with Asymptotically Constant Operator Coefficient

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We study the problem of existence of a unique bounded solution for a difference equation on the half axis with asymptotically constant operator coefficients in a Banach space. Necessary and sufficient conditions for the existence and uniqueness of bounded solutions are obtained for equations with and without initial condition.

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Authors and Affiliations

  1. T. Shevchenko Kyiv National University, Akad. Glushkov Ave., 4e, Kyiv, 03127, Ukraine

    A. V. Chaikovs’kyi

  2. Kyiv National University of Technologies and Design, Nemyrovych-Danchenko Str., 2, Kyiv, 01011, Ukraine

    O. A. Lagoda

Authors
  1. A. V. Chaikovs’kyi
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  2. O. A. Lagoda
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Correspondence to A. V. Chaikovs’kyi.

Additional information

Translated from Neliniini Kolyvannya, Vol. 24, No. 3, pp. 401–408, July–September, 2021.

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Chaikovs’kyi, A.V., Lagoda, O.A. Bounded Solutions of Difference Equations in a Banach Space with Asymptotically Constant Operator Coefficient. J Math Sci 272, 307–315 (2023). https://doi.org/10.1007/s10958-023-06418-w

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  • DOI: https://doi.org/10.1007/s10958-023-06418-w

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