# Oscillation Criterion for Autonomous Differential Equations with Bounded Aftereffect

## Abstract

For autonomous functional-differential equations with delays, we obtain an oscillation criterion, which allows one to reduce the oscillation problem to the calculation of a unique root of a real-valued function determined by the coefficients of the original equation. The criterion is illustrated by examples of equations with concentrated and distributed aftereffect, for which convenient oscillation tests are obtained.

- Authors:

- Perm National Research Polytechnic University (Russian Federation)

- Publication Date:

- OSTI Identifier:
- 22771279

- 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; FUNCTIONS; OSCILLATIONS

### Citation Formats

```
Malygina, V. V., E-mail: mavera@list.ru.
```*Oscillation Criterion for Autonomous Differential Equations with Bounded Aftereffect*. United States: N. p., 2018.
Web. doi:10.1007/S10958-018-3776-2.

```
Malygina, V. V., E-mail: mavera@list.ru.
```*Oscillation Criterion for Autonomous Differential Equations with Bounded Aftereffect*. United States. doi:10.1007/S10958-018-3776-2.

```
Malygina, V. V., E-mail: mavera@list.ru. Tue .
"Oscillation Criterion for Autonomous Differential Equations with Bounded Aftereffect". United States. doi:10.1007/S10958-018-3776-2.
```

```
@article{osti_22771279,
```

title = {Oscillation Criterion for Autonomous Differential Equations with Bounded Aftereffect},

author = {Malygina, V. V., E-mail: mavera@list.ru},

abstractNote = {For autonomous functional-differential equations with delays, we obtain an oscillation criterion, which allows one to reduce the oscillation problem to the calculation of a unique root of a real-valued function determined by the coefficients of the original equation. The criterion is illustrated by examples of equations with concentrated and distributed aftereffect, for which convenient oscillation tests are obtained.},

doi = {10.1007/S10958-018-3776-2},

journal = {Journal of Mathematical Sciences},

issn = {1072-3374},

number = 5,

volume = 230,

place = {United States},

year = {2018},

month = {5}

}

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