# On the periodic solutions of the Michelson continuous and discontinuous piecewise linear differential system

## Abstract

Applying new results from the averaging theory for continuous and discontinuous differential systems, we study the periodic solutions of two distinct versions of the Michelson differential system: a Michelson continuous piecewise linear differential system and a Michelson discontinuous piecewise linear differential system. The tools here used can be applied to general nonsmooth differential systems.

- Authors:

- Universitat Autònoma de Barcelona, Departament de Matemàtiques (Spain)
- ICMC-Universidade de São Paulo, Departamento de Matemática (Brazil)

- Publication Date:

- OSTI Identifier:
- 22769337

- Resource Type:
- Journal Article

- Journal Name:
- Computational and Applied Mathematics

- Additional Journal Information:
- Journal Volume: 37; Journal Issue: 2; Other Information: Copyright (c) 2018 SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0101-8205

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 97 MATHEMATICAL METHODS AND COMPUTING; DIFFERENTIAL EQUATIONS; MATHEMATICAL SOLUTIONS; PERIODICITY

### Citation Formats

```
Llibre, Jaume, Oliveira, Regilene, and Rodrigues, Camila Ap. B.,.
```*On the periodic solutions of the Michelson continuous and discontinuous piecewise linear differential system*. United States: N. p., 2018.
Web. doi:10.1007/S40314-016-0413-X.

```
Llibre, Jaume, Oliveira, Regilene, & Rodrigues, Camila Ap. B.,.
```*On the periodic solutions of the Michelson continuous and discontinuous piecewise linear differential system*. United States. doi:10.1007/S40314-016-0413-X.

```
Llibre, Jaume, Oliveira, Regilene, and Rodrigues, Camila Ap. B.,. Tue .
"On the periodic solutions of the Michelson continuous and discontinuous piecewise linear differential system". United States. doi:10.1007/S40314-016-0413-X.
```

```
@article{osti_22769337,
```

title = {On the periodic solutions of the Michelson continuous and discontinuous piecewise linear differential system},

author = {Llibre, Jaume and Oliveira, Regilene and Rodrigues, Camila Ap. B.,},

abstractNote = {Applying new results from the averaging theory for continuous and discontinuous differential systems, we study the periodic solutions of two distinct versions of the Michelson differential system: a Michelson continuous piecewise linear differential system and a Michelson discontinuous piecewise linear differential system. The tools here used can be applied to general nonsmooth differential systems.},

doi = {10.1007/S40314-016-0413-X},

journal = {Computational and Applied Mathematics},

issn = {0101-8205},

number = 2,

volume = 37,

place = {United States},

year = {2018},

month = {5}

}

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