On the Properties of Rings of Integro-Differential Operators and Their Corresponding Equations

The paper deals with systems of linear integro-differential equations, including systems with a matrix identically degenerate in the domain at the highest derivative of the unknown vector function. A theorem on the solvability of such systems of equations is proved. On the basis of this theorem, it...

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Bibliographic Details
Published in:Mathematical Notes 2022-08, Vol.112 (1-2), p.303-308
Main Author: Chistyakov, V. F.
Format: Article
Language:English
Subjects:
14/34
639/766/189
639/766/530
639/766/747
Differential equations
Mathematical analysis
Mathematics
Mathematics and Statistics
Operators (mathematics)
Theorems
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Summary:The paper deals with systems of linear integro-differential equations, including systems with a matrix identically degenerate in the domain at the highest derivative of the unknown vector function. A theorem on the solvability of such systems of equations is proved. On the basis of this theorem, it is shown that the ring of operators corresponding to these systems contains the semigroup of operators for which a left inverse operator from this ring is found.
ISSN:0001-4346
1067-9073
1573-8876
DOI:10.1134/S0001434622070331