# On the Solvability of a Matrix Boundary-Value Problem

## Abstract

We found solvability conditions and a construction of the generalized Green operator for a linear matrix boundary-value problem; we present an operator that reduces a linear matrix equation to the conventional linear Noether boundary-value problem. To solve a linear matrix system, we use the operator that reduces a linear matrix equation to a linear algebraic equation with a rectangular matrix.

- Authors:

- Donbass State Pedagogical University (Ukraine)

- Publication Date:

- OSTI Identifier:
- 22771265

- Resource Type:
- Journal Article

- Journal Name:
- Journal of Mathematical Sciences

- Additional Journal Information:
- Journal Volume: 230; Journal Issue: 5; Conference: International symposium on differential equations, Perm (Russian Federation), 17-18 May 2016; Other Information: Copyright (c) 2018 Springer Science+Business Media, LLC, part of Springer Nature; http://www.springer-ny.com; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1072-3374

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 97 MATHEMATICAL METHODS AND COMPUTING; BOUNDARY-VALUE PROBLEMS; DIFFERENTIAL EQUATIONS; GREEN FUNCTION; MATHEMATICAL OPERATORS; MATRICES

### Citation Formats

```
Chuiko, S. M., E-mail: chujko-slav@inbox.ru.
```*On the Solvability of a Matrix Boundary-Value Problem*. United States: N. p., 2018.
Web. doi:10.1007/S10958-018-3792-2.

```
Chuiko, S. M., E-mail: chujko-slav@inbox.ru.
```*On the Solvability of a Matrix Boundary-Value Problem*. United States. doi:10.1007/S10958-018-3792-2.

```
Chuiko, S. M., E-mail: chujko-slav@inbox.ru. Tue .
"On the Solvability of a Matrix Boundary-Value Problem". United States. doi:10.1007/S10958-018-3792-2.
```

```
@article{osti_22771265,
```

title = {On the Solvability of a Matrix Boundary-Value Problem},

author = {Chuiko, S. M., E-mail: chujko-slav@inbox.ru},

abstractNote = {We found solvability conditions and a construction of the generalized Green operator for a linear matrix boundary-value problem; we present an operator that reduces a linear matrix equation to the conventional linear Noether boundary-value problem. To solve a linear matrix system, we use the operator that reduces a linear matrix equation to a linear algebraic equation with a rectangular matrix.},

doi = {10.1007/S10958-018-3792-2},

journal = {Journal of Mathematical Sciences},

issn = {1072-3374},

number = 5,

volume = 230,

place = {United States},

year = {2018},

month = {5}

}

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