# Exact Conditions of Oscillation of Solutions to Differential Equations with Several Delays

## Abstract

We obtain new nonimprovable conditions of oscillation of all solutions to a linear differential equation with several variable delays and positive coefficients. These conditions have the form of the upper and lower limits of the sum of integrals of the coefficients over the sets that are determined only by the delay corresponding to this coefficient. These results differ from the well-known results in which a coarsening of the integration set is assumed.

- Authors:

- Perm National Research Polytechnic University (Russian Federation)

- Publication Date:

- OSTI Identifier:
- 22771266

- 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; INTEGRALS; MATHEMATICAL SOLUTIONS; OSCILLATIONS

### Citation Formats

```
Chudinov, K. M., E-mail: cyril@list.ru.
```*Exact Conditions of Oscillation of Solutions to Differential Equations with Several Delays*. United States: N. p., 2018.
Web. doi:10.1007/S10958-018-3791-3.

```
Chudinov, K. M., E-mail: cyril@list.ru.
```*Exact Conditions of Oscillation of Solutions to Differential Equations with Several Delays*. United States. doi:10.1007/S10958-018-3791-3.

```
Chudinov, K. M., E-mail: cyril@list.ru. Tue .
"Exact Conditions of Oscillation of Solutions to Differential Equations with Several Delays". United States. doi:10.1007/S10958-018-3791-3.
```

```
@article{osti_22771266,
```

title = {Exact Conditions of Oscillation of Solutions to Differential Equations with Several Delays},

author = {Chudinov, K. M., E-mail: cyril@list.ru},

abstractNote = {We obtain new nonimprovable conditions of oscillation of all solutions to a linear differential equation with several variable delays and positive coefficients. These conditions have the form of the upper and lower limits of the sum of integrals of the coefficients over the sets that are determined only by the delay corresponding to this coefficient. These results differ from the well-known results in which a coarsening of the integration set is assumed.},

doi = {10.1007/S10958-018-3791-3},

journal = {Journal of Mathematical Sciences},

issn = {1072-3374},

number = 5,

volume = 230,

place = {United States},

year = {2018},

month = {5}

}

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