Matematičeskie zametki, Tome 16 (1974) no. 2, pp. 259-265
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I. V. Kamenev. A necessary and sufficient condition for nonoscillatory behavior of the solutions of a system of two linear equations of the first order. Matematičeskie zametki, Tome 16 (1974) no. 2, pp. 259-265. http://geodesic.mathdoc.fr/item/MZM_1974_16_2_a9/
@article{MZM_1974_16_2_a9,
author = {I. V. Kamenev},
title = {A~necessary and sufficient condition for nonoscillatory behavior of the solutions of a~system of two linear equations of the first order},
journal = {Matemati\v{c}eskie zametki},
pages = {259--265},
year = {1974},
volume = {16},
number = {2},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/MZM_1974_16_2_a9/}
}
TY - JOUR
AU - I. V. Kamenev
TI - A necessary and sufficient condition for nonoscillatory behavior of the solutions of a system of two linear equations of the first order
JO - Matematičeskie zametki
PY - 1974
SP - 259
EP - 265
VL - 16
IS - 2
UR - http://geodesic.mathdoc.fr/item/MZM_1974_16_2_a9/
LA - ru
ID - MZM_1974_16_2_a9
ER -
%0 Journal Article
%A I. V. Kamenev
%T A necessary and sufficient condition for nonoscillatory behavior of the solutions of a system of two linear equations of the first order
%J Matematičeskie zametki
%D 1974
%P 259-265
%V 16
%N 2
%U http://geodesic.mathdoc.fr/item/MZM_1974_16_2_a9/
%G ru
%F MZM_1974_16_2_a9
For the system $y'=b(x)z$, $z'=-a(x)y$, where $a(x),b(x)\in C(x_0,+\infty)$, $b(x)\ge0$ we obtain for $x\ge x_0$ a necessary and sufficient condition for nonoscillatory behavior. From this condition we derive new criteria for the nonoscillatory behavior of the system considered.
