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Bounded in the mean solutions of a second-order difference equation
Volume 8, Issue 4 (2021), pp. 465–473
Mykhailo Horodnii   Victoriia Kravets ORCID icon link to view author Victoriia Kravets details  

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https://doi.org/10.15559/21-VMSTA189
Pub. online: 9 September 2021      Type: Research Article      Open accessOpen Access

Received
9 June 2021
Revised
9 August 2021
Accepted
17 August 2021
Published
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

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Dorogovtsev, A.Y.: Periodicheskie i statsionarnye rezhimy beskonechnomernykh determinirovannykh i stokhasticheskikh dinamicheskikh sistem, p. 320. “Vishcha Shkola”, Kiev (1992). MR1206004
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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
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Keywords
Difference equation bounded in the mean solution stationary solution proximity of solutions

MSC2010
60H99 39A10

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