An equation is derived for determining the characteristic exponents of a system of linear differential equations with coefficients depending on a random Markov periodic process at parametric resonance and using it, sufficient conditions for the existence of an unstable solution to the system are derived.

1.
J.
Diblík
,
I.
Dzhalladova
,
M.
Michalková
,
M.
Růžičková
,
Moment equations in modeling a stable foreign currency exchange market in conditions of uncertainty
,
Abstr. Appl. Anal
.
2013
(
2013
), Art. ID 172847, 11 pp.
2.
E.
Mathieu
,
M’emoire sur le mouvement vibratoire d’une membrane de forme elliptique
,
J. Math. Pures Appl
.
13
(ser. 2), (
1868
),
137203
.
3.
M.
Růžičková
,
I.
Dzhalladova
,
Dynamical systems with random structure and its applications, Stability, Oscillations and Optimization of Systems
vol.
10
,
Cambridge Scientific Publishers
,
2020
.
4.
K.G.
Valeev
:
On one method of solving a system of linear differential equations with sinusoidal coefficients
,
Izv. vuzov, Radiotekhnika
3
(
1960
),
1113
1126
. (in Russian)
5.
K.G.
Valeev
,
I.A.
Dzhalladova
:
Operating calculus and its application
, KNEU, Kyiv,
2002
. (in Ukrainian)
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