On bounded solutions of linear systems of differential equations with unbounded coefficients
This paper deals with a problem of finding a bounded solution of a system of nonhomogeneous linear differential equations with an unbounded matrix of coefficients on a finite interval. The right-hand side of the equation belongs to a space of continuous functions bounded with some weight; t...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Academician Ye.A. Buketov Karaganda University
2022-12-01
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| Series: | Қарағанды университетінің хабаршысы. Математика сериясы |
| Online Access: | https://mathematics-vestnik.ksu.kz/apart/2022-108-4/10.pdf |
| _version_ | 1797687499322032128 |
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| author | R.Ye. Uteshova Ye.V. Kokotova |
| author_facet | R.Ye. Uteshova Ye.V. Kokotova |
| author_sort | R.Ye. Uteshova |
| collection | DOAJ |
| description | This paper deals with a problem of finding a bounded solution of a system of nonhomogeneous linear differential equations with an unbounded matrix of coefficients on a finite interval. The right-hand side of the equation belongs to a space of continuous functions bounded with some weight; the weight function is chosen taking into account the behavior of the coefficient matrix. The problem is studied using a modified version of the parameterization method with non-uniform partitioning. Necessary and sufficient conditions of well-posedness of the problem are obtained in terms of a bilaterally infinite matrix of special structure. |
| first_indexed | 2024-03-12T01:18:51Z |
| format | Article |
| id | doaj.art-b967f27e7c024c6182c5a5db886a7691 |
| institution | Directory Open Access Journal |
| issn | 2518-7929 2663-5011 |
| language | English |
| last_indexed | 2024-03-12T01:18:51Z |
| publishDate | 2022-12-01 |
| publisher | Academician Ye.A. Buketov Karaganda University |
| record_format | Article |
| series | Қарағанды университетінің хабаршысы. Математика сериясы |
| spelling | doaj.art-b967f27e7c024c6182c5a5db886a76912023-09-13T09:53:24ZengAcademician Ye.A. Buketov Karaganda UniversityҚарағанды университетінің хабаршысы. Математика сериясы2518-79292663-50112022-12-01108410711610.31489/2022M4/107-116On bounded solutions of linear systems of differential equations with unbounded coefficientsR.Ye. UteshovaYe.V. Kokotova This paper deals with a problem of finding a bounded solution of a system of nonhomogeneous linear differential equations with an unbounded matrix of coefficients on a finite interval. The right-hand side of the equation belongs to a space of continuous functions bounded with some weight; the weight function is chosen taking into account the behavior of the coefficient matrix. The problem is studied using a modified version of the parameterization method with non-uniform partitioning. Necessary and sufficient conditions of well-posedness of the problem are obtained in terms of a bilaterally infinite matrix of special structure.https://mathematics-vestnik.ksu.kz/apart/2022-108-4/10.pdf |
| spellingShingle | R.Ye. Uteshova Ye.V. Kokotova On bounded solutions of linear systems of differential equations with unbounded coefficients Қарағанды университетінің хабаршысы. Математика сериясы |
| title | On bounded solutions of linear systems of differential equations with unbounded coefficients |
| title_full | On bounded solutions of linear systems of differential equations with unbounded coefficients |
| title_fullStr | On bounded solutions of linear systems of differential equations with unbounded coefficients |
| title_full_unstemmed | On bounded solutions of linear systems of differential equations with unbounded coefficients |
| title_short | On bounded solutions of linear systems of differential equations with unbounded coefficients |
| title_sort | on bounded solutions of linear systems of differential equations with unbounded coefficients |
| url | https://mathematics-vestnik.ksu.kz/apart/2022-108-4/10.pdf |
| work_keys_str_mv | AT ryeuteshova onboundedsolutionsoflinearsystemsofdifferentialequationswithunboundedcoefficients AT yevkokotova onboundedsolutionsoflinearsystemsofdifferentialequationswithunboundedcoefficients |