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Bounded Solutions of Difference Equations in a Banach Space with Input Data from Subspaces

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Ukrainian Mathematical Journal Aims and scope

We study the problem of existence and uniqueness of a bounded solution to a difference equation of the first order with constant operator coefficient in a Banach space. We establish necessary and sufficient conditions for the case where the initial condition and the input sequence belong to certain subspaces. These results are applied to the case of difference equations with a jump of the operator coefficient and difference equations of higher orders.

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Author information

Authors and Affiliations

  1. T. Shevchenko Kyiv National University, Kyiv, Ukraine

    A.V. Chaikovs’kyi

  2. Kyiv National University of Technologies and Design, Kyiv, Ukraine

    O. A. Lagoda

Authors
  1. A.V. Chaikovs’kyi
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  2. O. A. Lagoda
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Corresponding author

Correspondence to A.V. Chaikovs’kyi.

Additional information

Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 73, No. 11, pp. 1564–1575, November, 2021. Ukrainian DOI: https://doi.org/10.37863/umzh.v73i11.6692.

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Chaikovs’kyi, A., Lagoda, O.A. Bounded Solutions of Difference Equations in a Banach Space with Input Data from Subspaces. Ukr Math J 73, 1810–1824 (2022). https://doi.org/10.1007/s11253-022-02031-3

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  • DOI: https://doi.org/10.1007/s11253-022-02031-3

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