# On a Certain First-Order Differential Equation with Delay

## Abstract

We consider the Cauchy problem for a first-order quasilinear differential equation with delayed argument of neutral type, and obtain sufficient conditions of existence and uniqueness of its solutions. Proofs of the solvability of nonlinear problems, estimates of solutions, and constructions of approximate methods are based on Chaplygin-type theorems on differential inequalities.

- Authors:

- Bratsk State University (Russian Federation)

- Publication Date:

- OSTI Identifier:
- 22771281

- 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; APPROXIMATIONS; CAUCHY PROBLEM; DIFFERENTIAL EQUATIONS; MATHEMATICAL SOLUTIONS; NONLINEAR PROBLEMS

### Citation Formats

```
Larionov, A. S., E-mail: larios84@yandex.ru.
```*On a Certain First-Order Differential Equation with Delay*. United States: N. p., 2018.
Web. doi:10.1007/S10958-018-3774-4.

```
Larionov, A. S., E-mail: larios84@yandex.ru.
```*On a Certain First-Order Differential Equation with Delay*. United States. doi:10.1007/S10958-018-3774-4.

```
Larionov, A. S., E-mail: larios84@yandex.ru. Tue .
"On a Certain First-Order Differential Equation with Delay". United States. doi:10.1007/S10958-018-3774-4.
```

```
@article{osti_22771281,
```

title = {On a Certain First-Order Differential Equation with Delay},

author = {Larionov, A. S., E-mail: larios84@yandex.ru},

abstractNote = {We consider the Cauchy problem for a first-order quasilinear differential equation with delayed argument of neutral type, and obtain sufficient conditions of existence and uniqueness of its solutions. Proofs of the solvability of nonlinear problems, estimates of solutions, and constructions of approximate methods are based on Chaplygin-type theorems on differential inequalities.},

doi = {10.1007/S10958-018-3774-4},

journal = {Journal of Mathematical Sciences},

issn = {1072-3374},

number = 5,

volume = 230,

place = {United States},

year = {2018},

month = {5}

}

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