Bounded and summable solutions of a difference equation with piecewise constant operator coefficients
Abstract
UDC 517.929.2
We prove the necessity of known sufficient conditions for the existence of a unique solution bounded or summable with degree $p$ for a linear difference equation with piecewise constant operator coefficients.
References
Yu. L. Daleckij, M. G. Kreĭn, Ustojchivost' reshenij differencial'nyh uravnenij v banahovom prostranstve, Nauka, Moskva (1970).
I. V. Gonchar, Pro obmezheni i sumovni rozv’yazki riznicevogo rivnyannya zi stribkom operatornogo koeficiєnta, Visn. Kyiv. nac. un-tu im. T. Shevchenka. Ser. fiz.-mat. nauki, № 2, 25 – 28 (2016).
M. F. Horodnii, I. V. Gonchar, Pro obmezheni rozv’yazki riznicevogo rivnyannya zi zminnim operatornim koeficiєntom, Dop. NAN Ukraїni, № 12, 12 – 16 (2016).
A. G. Baskakov, A. I. Pastuhov, Spektral'nyj analiz operatora vzveshennogo sdviga s neogranichennymi operatornymi koefficientami, Sib. mat. zhurn., 42, № 6, 1231 – 1243 (2001).
V. YU. Slyusarchuk, Eksponencial'no dihotomichni riznicevi rivnyannya z kuskovo-stalimi operatornimi koeficiєntami, Ukr. mat. zhurn., 72, № 6, 822 – 841 (2020). DOI: https://doi.org/10.37863/umzh.v72i6.1052
M. F. Gorodnij, O. A. Pechericya, Obmezheni rozv’yazki diferencial'nogo rivnyannya z kuskovo-stalimi operatornimi koeficiєntami, Nelinijni kolivannya, 24, № 2, 147 – 157 (2021).
A. V. Chaikovs'kyi, O. A. Lagoda, Bounded solutions of a difference equation in Banach space with input data in subspaces, Ukr. mat. zhurn.,, 73, № 11, 1564 – 1575 (2021), https://doi.org/10.37863/umzh.v73i11.6692 DOI: https://doi.org/10.1007/s11253-022-02031-3
V. YU. Slyusarchuk, Ob eksponencial'noj dihotomii reshenij diskretnyh sistem, Ukr. mat. zhurn.,35, № 1, 109 – 115 (1983).
D. Henri, Geometricheskaya teoriya polulinejnyh parabolicheskih uravnenij, Mir, Moskva (1985).
A. YA. Dorogovcev, Periodicheskie i stacionarnye rezhimy beskonechnomernyh determinirovannyh i stohasticheskih dinamicheskih sistem, Vishcha shk., Kiev (1992).
A. A. Boichuk, A. M. Samoilenko, Generalized inverse operators and Fredholm boundary value problems, VSP, Utrecht, Boston (2004), https://doi.org/10.1515/9783110944679 DOI: https://doi.org/10.1515/9783110944679
A. G. Baskakov, Issledovanie linejnyh differencial'nyh uravnenij metodami spektral'noj teorii raznostnyh operatorov i linejnyh otnoshenij, Uspekhi mat. nauk, 68, vyp. 1(409), 77 – 128 (2013). DOI: https://doi.org/10.4213/rm9505
M. F. Horodnii, Ogranichennye i periodicheskie resheniya odnogo raznostnogo uravneniya i ego stohasticheskogo analoga v banahovom prostranstve, Ukr. mat. zhurn.,43, № 1, 41 – 46 (1991).
M. F. Horodnii, I. V. Gonchar, Obmezheni u seredn'omu poryadku p rozv’yazki riznicevogo rivnyannya zi stribkom operatornogo koeficiєnta, Teoriya jmovirnostej ta mat. statistika, vip. 2(101), 93 – 97 (2019).
M. Horodnii, V. Kravets, Bounded in the mean solutions of a second-order difference equation, Modern Stochastics: Theory and Appl., 8, № 4, 465 – 474 (2021), https://doi.org/10.15559/21-VMSTA189 DOI: https://doi.org/10.15559/21-VMSTA189
Copyright (c) 2022 Михайло Федорович Городній
This work is licensed under a Creative Commons Attribution 4.0 International License.