Geodesic
On the Aizerman Problem for Systems of Two Differential Equations
Matematičeskie zametki, Tome 105 (2019) no. 2, pp. 240-250

Voir la notice de l'article provenant de la source Math-Net.Ru

The stability of equilibria of systems of nonlinear ordinary differential equations is studied. A criterion for the reducibility of a second-order linear system to a scalar differential equation is given. Both positive definite and semidefinite Lyapunov functions are used to obtain sufficient conditions for the asymptotic stability (global stability) of second-order nonlinear differential equations. It is proved that the Aizerman problem has a positive solution with respect to the roots of the characteristic equation of two-dimensional systems of differential equations.
Keywords: system of differential equations, equilibrium, stability, Aizerman problem, Lyapunov functions. 
@article{MZM_2019_105_2_a5,
     author = {B. S. Kalitin},
     title = {On the {Aizerman} {Problem} for {Systems} of {Two} {Differential} {Equations}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {240--250},
     publisher = {mathdoc},
     volume = {105},
     number = {2},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2019_105_2_a5/}
}
TY  - JOUR
AU  - B. S. Kalitin
TI  - On the Aizerman Problem for Systems of Two Differential Equations
JO  - Matematičeskie zametki
PY  - 2019
SP  - 240
EP  - 250
VL  - 105
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2019_105_2_a5/
LA  - ru
ID  - MZM_2019_105_2_a5
ER  - 
%0 Journal Article
%A B. S. Kalitin
%T On the Aizerman Problem for Systems of Two Differential Equations
%J Matematičeskie zametki
%D 2019
%P 240-250
%V 105
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2019_105_2_a5/
%G ru
%F MZM_2019_105_2_a5
B. S. Kalitin. On the Aizerman Problem for Systems of Two Differential Equations. Matematičeskie zametki, Tome 105 (2019) no. 2, pp. 240-250. http://geodesic.mathdoc.fr/item/MZM_2019_105_2_a5/