# Asymptotics of Oscillating Solutions to Equations with Power Nonlinearities

## Abstract

We present results on the existence of oscillating solutions of specific form (“quasiperiodic solutions) for a nonlinear differential equation with power nonlinearity. For oscillating solutions to third-order equations of this type, we obtain an asymptotics of extremums, which is expressed through the asymptotics of extremums of a “quasiperiodic” solution. These results clarify the asymptotic formulas for the modules of extremums of solutions obtained by the author earlier.

- Authors:

- M. V. Lomonosov Moscow State University (Russian Federation)

- Publication Date:

- OSTI Identifier:
- 22771293

- 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; ASYMPTOTIC SOLUTIONS; DIFFERENTIAL EQUATIONS; NONLINEAR PROBLEMS; PERIODICITY

### Citation Formats

```
Astashova, I. V., E-mail: ast@diffiety.ac.ru.
```*Asymptotics of Oscillating Solutions to Equations with Power Nonlinearities*. United States: N. p., 2018.
Web. doi:10.1007/S10958-018-3762-8.

```
Astashova, I. V., E-mail: ast@diffiety.ac.ru.
```*Asymptotics of Oscillating Solutions to Equations with Power Nonlinearities*. United States. doi:10.1007/S10958-018-3762-8.

```
Astashova, I. V., E-mail: ast@diffiety.ac.ru. Tue .
"Asymptotics of Oscillating Solutions to Equations with Power Nonlinearities". United States. doi:10.1007/S10958-018-3762-8.
```

```
@article{osti_22771293,
```

title = {Asymptotics of Oscillating Solutions to Equations with Power Nonlinearities},

author = {Astashova, I. V., E-mail: ast@diffiety.ac.ru},

abstractNote = {We present results on the existence of oscillating solutions of specific form (“quasiperiodic solutions) for a nonlinear differential equation with power nonlinearity. For oscillating solutions to third-order equations of this type, we obtain an asymptotics of extremums, which is expressed through the asymptotics of extremums of a “quasiperiodic” solution. These results clarify the asymptotic formulas for the modules of extremums of solutions obtained by the author earlier.},

doi = {10.1007/S10958-018-3762-8},

journal = {Journal of Mathematical Sciences},

issn = {1072-3374},

number = 5,

volume = 230,

place = {United States},

year = {2018},

month = {5}

}

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