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

1Gorodnii, MF
Kravets, VP
1Taras Shevchenko National University of Kyiv
Dopov. Nac. akad. nauk Ukr. 2019, 2:12-16
Section: Mathematics
Language: Ukrainian

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.

Keywords: bounded solution, difference equation, finitedimensional space, linear operator

1. 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:
2. Dorogovtsev, A. Ya. (1992). Periodic and stationary regimes of infinitedimensional deterministic and stochastic dynamical systems. Kiev: Vyshcha Shkola (in Ukrainian).
3. 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:
4. Shabat, B. V. (1985). Introduction to complex analysis. Part 1: Function of one variable. University textbook. 3th ed. Mosñow: Nauka (in Russian).