Bounded in the mean solutions of a second-order difference equation
Volume 8, Issue 4 (2021), pp. 465–473
Pub. online: 9 September 2021
Type: Research Article
Open Access
Open Access
Received
9 June 2021
9 June 2021
Revised
9 August 2021
9 August 2021
Accepted
17 August 2021
17 August 2021
Published
9 September 2021
9 September 2021
Abstract
Sufficient conditions are given for the existence of a unique bounded in the mean solution to a second-order difference equation with jumps of operator coefficients in a Banach space. The question of the proximity of this solution to the stationary solution of the corresponding difference equation with constant operator coefficients is studied.
References
Baskakov, A.G.: On the invertibility of linear difference operators with constant coefficients. Izv. Vysš. Učebn. Zaved., Mat. 5, 3–11 (2001). MR1860652
Dorogovtsev, A.Y.: Stationary and periodic solutions of a stochastic difference equation in a Banach space. Teor. Veroyatn. Mat. Stat. 42, 35–42 (1990). MR1069311
Dorogovtsev, A.Y.: Periodicheskie i statsionarnye rezhimy beskonechnomernykh determinirovannykh i stokhasticheskikh dinamicheskikh sistem, p. 320. “Vishcha Shkola”, Kiev (1992). MR1206004
Gorodnii, M., Gonchar, I.: Bounded in the mean of order p solutions of a difference equation with a jump of the operator coefficient. Theory Probab. Math. Stat. 101, 103–108 (2020) MR3671867. https://doi.org/10.1007/s10958-018-3685-4
Gorodnı¯ĭ, M.F., Kravets’, V.P.: On bounded solutions of a second-order difference equation. Nelı¯nı¯ĭnı¯ Koliv. 22(2), 196–201 (2019). MR3969788
Henry, D.: Geometric Theory of Semilinear Parabolic Equations. Lecture Notes in Mathematics, vol. 840, p. 348. Springer (1981). MR610244
Kabantsova, L.Y.: Second-order linear difference equations in a Banach space and the splitting of operators. Izv. Sarat. Univ. (N.S.), Ser. Mat. Mekh. Inform. 17(3), 285–293 (2017). doi: https://doi.org/10.18500/1816-9791-2017-17-3-285-293. MR3697884
Morozan, T.: Bounded, periodic and almost periodic solutions of affine stochastic discrete-time systems. Rev. Roum. Math. Pures Appl. 32(8), 711–718 (1987). MR917687
Slyusarchuk, V.E.: Invertibility of linear nonautonomous difference operators in the space of bounded functions on Z. Mat. Zametki 37(5), 662–666780 (1985). MR797706
