# The Bohl–Perron Theorem for Hybrid Linear Systems with Aftereffect

## Abstract

We consider an abstract hybrid system of functional-differential equations. Both equations are functional-differential with respect to one part of variables and difference with respect to to the other part of variables. To the system of two equations with two unknowns appeared, we apply the W-method of N. V. Azbelev. We examine two models: a system of functional-differential equations and a system of difference equations. We study the spaces of their solutions and obtain the Bohl–Perron-type theorems on the exponential stability.

- Authors:

- Perm State National Research University (Russian Federation)

- Publication Date:

- OSTI Identifier:
- 22771268

- 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; DIFFERENTIAL EQUATIONS; HYBRID SYSTEMS; MATHEMATICAL SOLUTIONS; MATHEMATICAL SPACE; STABILITY

### Citation Formats

```
Simonov, P. M., E-mail: simpm@mail.ru.
```*The Bohl–Perron Theorem for Hybrid Linear Systems with Aftereffect*. United States: N. p., 2018.
Web. doi:10.1007/S10958-018-3788-Y.

```
Simonov, P. M., E-mail: simpm@mail.ru.
```*The Bohl–Perron Theorem for Hybrid Linear Systems with Aftereffect*. United States. doi:10.1007/S10958-018-3788-Y.

```
Simonov, P. M., E-mail: simpm@mail.ru. Tue .
"The Bohl–Perron Theorem for Hybrid Linear Systems with Aftereffect". United States. doi:10.1007/S10958-018-3788-Y.
```

```
@article{osti_22771268,
```

title = {The Bohl–Perron Theorem for Hybrid Linear Systems with Aftereffect},

author = {Simonov, P. M., E-mail: simpm@mail.ru},

abstractNote = {We consider an abstract hybrid system of functional-differential equations. Both equations are functional-differential with respect to one part of variables and difference with respect to to the other part of variables. To the system of two equations with two unknowns appeared, we apply the W-method of N. V. Azbelev. We examine two models: a system of functional-differential equations and a system of difference equations. We study the spaces of their solutions and obtain the Bohl–Perron-type theorems on the exponential stability.},

doi = {10.1007/S10958-018-3788-Y},

journal = {Journal of Mathematical Sciences},

issn = {1072-3374},

number = 5,

volume = 230,

place = {United States},

year = {2018},

month = {5}

}

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