Matematičeskie zametki, Tome 17 (1975) no. 6, pp. 919-923
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V. E. Slyusarchuk. Sufficient conditions for absolute asymptotic stability of linear equations in a Banach space. Matematičeskie zametki, Tome 17 (1975) no. 6, pp. 919-923. http://geodesic.mathdoc.fr/item/MZM_1975_17_6_a9/
@article{MZM_1975_17_6_a9,
author = {V. E. Slyusarchuk},
title = {Sufficient conditions for absolute asymptotic stability of linear equations in {a~Banach} space},
journal = {Matemati\v{c}eskie zametki},
pages = {919--923},
year = {1975},
volume = {17},
number = {6},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/MZM_1975_17_6_a9/}
}
TY - JOUR
AU - V. E. Slyusarchuk
TI - Sufficient conditions for absolute asymptotic stability of linear equations in a Banach space
JO - Matematičeskie zametki
PY - 1975
SP - 919
EP - 923
VL - 17
IS - 6
UR - http://geodesic.mathdoc.fr/item/MZM_1975_17_6_a9/
LA - ru
ID - MZM_1975_17_6_a9
ER -
%0 Journal Article
%A V. E. Slyusarchuk
%T Sufficient conditions for absolute asymptotic stability of linear equations in a Banach space
%J Matematičeskie zametki
%D 1975
%P 919-923
%V 17
%N 6
%U http://geodesic.mathdoc.fr/item/MZM_1975_17_6_a9/
%G ru
%F MZM_1975_17_6_a9
For a linear differential equation of the type \begin{equation} \frac{dx}{dt}=A_0x(t)+A_1x(t-\Delta_1)+\dots+A_nx(t-\Delta_n)\tag{1} \end{equation} we establish the following \underline {THEOREM}. If $$ \overline{\bigcup_{|z_1|=\dots=|z_n|=1}\sigma\Bigl(A_0+\sum_{k=1}^nz_kA_k\Bigl)}\subset\{\lambda:\operatorname{Re}\lambda<0\}, $$ then system (1) is absolutely asymptotically stable.
