Approximation of a bounded solution of one difference equation with unbounded operator coefficient by solutions of the corresponding boundary-value problems
We investigate the problem of approximation of a bounded solution of a difference analog of the differential equation $$x^{(m)}(t) + A_1x^{(m-1)}(t) + ... + A_{m-1}x'(t)) = Ax(t) +f(0), t \in R$$ by solutions of the corresponding boundary-value problems. Here, A is an unbounded operator i...
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| Datum: | 2000 |
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| Sprache: | Ukrainisch Englisch |
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Institute of Mathematics, NAS of Ukraine
2000
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/4445 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860510571981438976 |
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| author | Gorodnii, M. F. Romanenko, V. N. Городній, М. Ф. Романенко, В. М. |
| author_facet | Gorodnii, M. F. Romanenko, V. N. Городній, М. Ф. Романенко, В. М. |
| author_sort | Gorodnii, M. F. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T20:29:03Z |
| description | We investigate the problem of approximation of a bounded solution of a difference analog of the differential equation $$x^{(m)}(t) + A_1x^{(m-1)}(t) + ... + A_{m-1}x'(t)) = Ax(t) +f(0), t \in R$$
by solutions of the corresponding boundary-value problems. Here, A is an unbounded operator in a Banach space B, {A 1,...,A m-1} ⊂L(B) and f:ℝ→B is a fixed function. |
| first_indexed | 2026-03-24T02:59:07Z |
| format | Article |
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| id | umjimathkievua-article-4445 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | Ukrainian English |
| last_indexed | 2026-03-24T02:59:07Z |
| publishDate | 2000 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/eb/698dfbdb1a0ada149e727bb6e9c263eb.pdf |
| spelling | umjimathkievua-article-44452020-03-18T20:29:03Z Approximation of a bounded solution of one difference equation with unbounded operator coefficient by solutions of the corresponding boundary-value problems Апроксимація обмежеиото розв'язку одпото різницевото рівняння з необмеженим операторпим коефіцієнтом розв'язками відповідних крайових задач Gorodnii, M. F. Romanenko, V. N. Городній, М. Ф. Романенко, В. М. We investigate the problem of approximation of a bounded solution of a difference analog of the differential equation $$x^{(m)}(t) + A_1x^{(m-1)}(t) + ... + A_{m-1}x'(t)) = Ax(t) +f(0), t \in R$$ by solutions of the corresponding boundary-value problems. Here, A is an unbounded operator in a Banach space B, {A 1,...,A m-1} ⊂L(B) and f:ℝ→B is a fixed function. Досліджено питання про апроксимацію обмеженого розв'язку різницевого аналога диференціального рівняння $$x^{(m)}(t) + A_1x^{(m-1)}(t) + ... + A_{m-1}x'(t)) = Ax(t) +f(0), t \in R$$ розв'язками відповідних крайових задач. Тут $А$ — необмежений оператор в банаховому просторі $B, \{A_1,...,A_{m-1}\} ⊂L(B),\$ $f : ℝ → B$ — фіксована функція. Institute of Mathematics, NAS of Ukraine 2000-04-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/4445 Ukrains’kyi Matematychnyi Zhurnal; Vol. 52 No. 4 (2000); 548-552 Український математичний журнал; Том 52 № 4 (2000); 548-552 1027-3190 uk en https://umj.imath.kiev.ua/index.php/umj/article/view/4445/5594 https://umj.imath.kiev.ua/index.php/umj/article/view/4445/5595 Copyright (c) 2000 Gorodnii M. F.; Romanenko V. N. |
| spellingShingle | Gorodnii, M. F. Romanenko, V. N. Городній, М. Ф. Романенко, В. М. Approximation of a bounded solution of one difference equation with unbounded operator coefficient by solutions of the corresponding boundary-value problems |
| title | Approximation of a bounded solution of one difference equation with unbounded operator coefficient by solutions of the corresponding boundary-value problems |
| title_alt | Апроксимація обмежеиото розв'язку одпото різницевото рівняння з необмеженим операторпим коефіцієнтом розв'язками відповідних крайових задач |
| title_full | Approximation of a bounded solution of one difference equation with unbounded operator coefficient by solutions of the corresponding boundary-value problems |
| title_fullStr | Approximation of a bounded solution of one difference equation with unbounded operator coefficient by solutions of the corresponding boundary-value problems |
| title_full_unstemmed | Approximation of a bounded solution of one difference equation with unbounded operator coefficient by solutions of the corresponding boundary-value problems |
| title_short | Approximation of a bounded solution of one difference equation with unbounded operator coefficient by solutions of the corresponding boundary-value problems |
| title_sort | approximation of a bounded solution of one difference equation with unbounded operator coefficient by solutions of the corresponding boundary-value problems |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/4445 |
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