TY - JOUR
T1 - Floquet theory and stability for a class of first order differential equations with delays
AU - Domoshnitsky, Alexander
AU - Berenson, Elnatan
AU - Levi, Shai
AU - Litsyn, Elena
N1 - Publisher Copyright:
© 2024 Walter de Gruyter GmbH, Berlin/Boston 2024.
PY - 2024
Y1 - 2024
N2 - A version of the Floquet theory for first order delay differential equations is proposed. Formula of solutions representation is obtained. On this basis, the stability of first order delay differential equations is studied. An analogue of the classical integral Lyapunov-Zhukovskii test of stability is proved. New, in comparison with all known, tests of the exponential stability are obtained on the basis of the Floquet theory. A possibility to achieve the exponential stability is connected with oscillation of solutions.
AB - A version of the Floquet theory for first order delay differential equations is proposed. Formula of solutions representation is obtained. On this basis, the stability of first order delay differential equations is studied. An analogue of the classical integral Lyapunov-Zhukovskii test of stability is proved. New, in comparison with all known, tests of the exponential stability are obtained on the basis of the Floquet theory. A possibility to achieve the exponential stability is connected with oscillation of solutions.
KW - Floquet theory
KW - comparison theorems
KW - delay differential equations
KW - exponential stability
KW - periodic coefficients and delays
UR - http://www.scopus.com/inward/record.url?scp=85181470436&partnerID=8YFLogxK
U2 - 10.1515/gmj-2023-2119
DO - 10.1515/gmj-2023-2119
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AN - SCOPUS:85181470436
SN - 1072-947X
JO - Georgian Mathematical Journal
JF - Georgian Mathematical Journal
ER -