Investigation of the Stability of Solutions of Systems of Ordinary Differential Equations

被引：0
作者：
Kadry, S. [1 ]
Alferov, G. [2 ]
Ivanov, G. [2 ]
Korolev, V [2 ]
机构：
[1] Beirut Arab Univ, Dept Math & Comp Sci, Beirut, Lebanon
[2] St Petersburg State Univ, St Petersburg, Russia
来源：
INTERNATIONAL CONFERENCE ON NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2019 | 2020年 / 2293卷
关键词：
differential equations; partial and external derived numbers; stability;
D O I：
10.1063/5.0026495
中图分类号：
Q [生物科学];
学科分类号：
07 ; 0710 ; 09 ;
摘要：
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 smootlmess 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.
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页数：4
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