The bounded solutions of a second•order difference equation with a jump of the operator coefficient

Authors

  • M.F. Gorodnii Taras Shevchenko National University of Kiev
  • V.P. Kravets Taras Shevchenko National University of Kiev

DOI:

https://doi.org/10.15407/dopovidi2019.02.012

Keywords:

bounded solution, difference equation, finitedimensional space, linear operator

Abstract

We study the problem of existence of the unique bounded solution of a linear secondorder difference equation with a jump of the operator coefficient in a finitedimensional Banach space. For such an equation, the criterion for the existence and uniqueness of a bounded solution is proved for any “input” bounded sequence. The case where the matrix of operator coefficients reduces to a diagonal form is investigated in detail.

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References

Gorodnii, M. F. & Gonchar, I. V. (2016). On the bounded solutions of a difference equation with variable operator coefficient. Dopov. Nac. akad. nauk. Ukr., No. 12, pp. 1216 (in Ukrainian). doi: https://doi.org/10.15407/dopovidi2016.12.012

Dorogovtsev, A. Ya. (1992). Periodic and stationary regimes of infinitedimensional deterministic and stochastic dynamical systems. Kiev: Vyshcha Shkola (in Ukrainian).

Kabantsova, L. Yu. (2017). Linear difference equation of second order in a banach space and operators splitting. Izv. Saratov. Univ. (N. S.) Ser. Math. Mech. Inform., 17, Iss.3, pp. 285293 (in Russian). doi: https://doi.org/10.18500/181697912017173285293

Shabat, B. V. (1985). Introduction to complex analysis. Part 1: Function of one variable. University textbook. 3th ed. Mosñow: Nauka (in Russian).

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Published

15.04.2024

How to Cite

Gorodnii, M., & Kravets, V. (2024). The bounded solutions of a second•order difference equation with a jump of the operator coefficient . Reports of the National Academy of Sciences of Ukraine, (2), 12–16. https://doi.org/10.15407/dopovidi2019.02.012

Issue

No. 2 (2019): Reports of the National Academy of Sciences of Ukraine

Section

Mathematics

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Copyright (c) 2024 Reports of the National Academy of Sciences of Ukraine

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