Bounded solutions of a difference equation in Banach space with input data in subspaces

  • A. V. Chaikovs'kyi Taras Shevchenko University of Kyiv
  • O. A. Lagoda Kyiv. nat. University of Technology and Design
Keywords: Difference equation, bounded solution, Banach space, subspace

Abstract

UDC 517.929.2

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

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Published
23.11.2021
How to Cite
Chaikovs’kyi, A. V., and O. A. Lagoda. “Bounded Solutions of a Difference Equation in Banach Space With Input Data in Subspaces”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 73, no. 11, Nov. 2021, pp. 1564 -75, doi:10.37863/umzh.v73i11.6692.
Section
Research articles