@inproceedings{781e02285e1c4dcdb028a20c04caebee,
title = "Investigation of the stability of solutions of systems of ordinary differential equations",
abstract = "An apparatus of partial and external derived numbers is proposed, which makes it possible to investigate the behavior of a function of several variables, without requiring its differentiability, but using only information about partial derived numbers, reducing restrictions on the degree of smoothness of the functions studied. The use of the apparatus of external derived numbers makes it possible to reduce the restrictions on the degree of smoothness of manifolds when studying the question of the integrability of the field of hyperplanes. The proposed method can be used to obtain the necessary or sufficient conditions for the stability of solutions of systems of differential equations. Using the apparatus of partial and external derived numbers, it can be shown that the investigation of the stability of solutions of a system of differential equations can be reduced to an investigation of the solvability of a system of equations of a special form.",
keywords = "Differential equations, Partial and external derived numbers, Stability",
author = "S. Kadry and G. Alferov and G. Ivanov and V. Korolev",
note = "Publisher Copyright: {\textcopyright} 2020 American Institute of Physics Inc.. All rights reserved.; International Conference on Numerical Analysis and Applied Mathematics 2019, ICNAAM 2019 ; Conference date: 23-09-2019 Through 28-09-2019",
year = "2020",
month = nov,
day = "24",
doi = "10.1063/5.0026495",
language = "English",
series = "AIP Conference Proceedings",
publisher = "American Institute of Physics Inc.",
editor = "Simos, \{Theodore E.\} and Simos, \{Theodore E.\} and Simos, \{Theodore E.\} and Simos, \{Theodore E.\} and Simos, \{Theodore E.\} and Charalambos Tsitouras",
booktitle = "International Conference on Numerical Analysis and Applied Mathematics, ICNAAM 2019",
}