| Title | The bounded solutions of a second•order difference equation with a jump of the operator coefficient |
| Publication Type | Journal Article |
| Year of Publication | 2019 |
| Authors | Gorodnii, MF, Kravets, VP |
| Abbreviated Key Title | Dopov. Nac. akad. nauk Ukr. |
| DOI | 10.15407/dopovidi2019.02.012 |
| Issue | 2 |
| Section | Mathematics |
| Pagination | 12-16 |
| Date Published | 02/2019 |
| Language | Ukrainian |
| 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. |
| 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: https://doi.org/10.15407/dopovidi2016.12.012
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: https://doi.org/10.18500/181697912017173285293
4. Shabat, B. V. (1985). Introduction to complex analysis. Part 1: Function of one variable. University textbook. 3th ed. Mosñow: Nauka (in Russian).
