Araştırma Makalesi

As Sir Isaac Newton has said, laws of the Nature have been written in the

language of Differential Equations. In particular, the classical theory of

normal systems of Ordinary Differential Equations, supported by Cauchy theorems

of existence and uniqueness of solutions, describes determined processes taking

place in the Nature, technics and even in the society, i.e. such processes, for

which a condition of a described system in an arbitrary fixed moment depends on

its condition in any other moment. Solutions, describing such processes, are called

the ordinary. But when the conditions of the Cauchy theorem are not satisfied,

a situation totally changes. A point, in any neighborhood of which such

conditions are not satisfied, may become for a system under consideration a

point of non-uniqueness, a point of bifurcation. A solution of a system, each

point of which appears to be a point of non-uniqueness, is called a special

solution. A task of a full integration of a system demands finding of all its

solutions, special solutions as well as ordinary ones. But this item shows us

some gap in a special literature. This paper presents materials with the aim to

fill this gap.

Differential equations Ordinary solution Special solution Bifurcations

- Andreev, A.F., & Andreeva, I.A. (2002). On a Question of Parametric Integration of Differential Equations. Vestnik St. Petersburg University: Ser.1. Mathematics, Mechanics, Astronomy, 4, 3- 10. Andreeva, I.A. (2003). Higher Mathematics. Special Solutions of Differential Equations of the First Order. St. Petersburg: SPbPU Publishing House. Andreev, A.F., & Andreeva, I.A. (2017). Investigation of a Family of Cubic Dynamic Systems. Vibroengineering Procedia, 15, 88 – 93. DOI: 10.21595/vp.2017.19389. Zalgaller, V.A. (1975). A Theory of Envelopes. Moscow: Nauka.

Yıl 2018,
Sayı: 2, 403 - 406, 19.08.2018
### Öz

### Kaynakça

Toplam 1 adet kaynakça vardır.

Birincil Dil | İngilizce |
---|---|

Konular | Mühendislik |

Bölüm | Makaleler |

Yazarlar | |

Yayımlanma Tarihi | 19 Ağustos 2018 |

Yayımlandığı Sayı | Yıl 2018Sayı: 2 |