Geodesic
Specific Features of the Study of Nonautonomous Differential Equations with Exponential-Type Matrices
Matematičeskie zametki, Tome 101 (2017) no. 2, pp. 226-231.

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An algorithm for the spectral analysis of nonautonomous systems of differential equations on the semiaxis whose matrix can be presented as the sum of exponential-type matrices is developed. This method, which is based on a version of the splitting method, allows us to prove a theorem stating that the initial system is almost reducible to a simpler equivalent system and to formulate a sufficient condition for the asymptotic stability and the stability of its trivial solution.
Keywords: nonautonomous system of ordinary differential equations, splitting method, asymptotic reducibility, stability. 
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Yu. A. Konyaev; D. A. Maslov. Specific Features of the Study of Nonautonomous Differential Equations with Exponential-Type Matrices. Matematičeskie zametki, Tome 101 (2017) no. 2, pp. 226-231. http://geodesic.mathdoc.fr/item/MZM_2017_101_2_a7/

[1] V. Vazov, Asimptoticheskie razlozheniya reshenii obyknovennykh differentsialnykh uravnenii, MIR, M., 1968 | Zbl

[2] B. P. Demidovich, Lektsii po matematicheskoi teorii ustoichivosti, Izd-vo Mosk. un-ta, M., 1998

[3] Yu. A. Konyaev, “O nekotorykh metodakh issledovaniya ustoichivosti”, Matem. sb., 192:3 (2001), 65–82 | DOI | MR | Zbl

[4] Yu. A. Konyaev, Yu. G. Martynenko, “Asimptoticheskii analiz reshenii differentsialnykh uravnenii s polinomialno periodicheskimi koeffitsientami”, Izv. vuzov. Matem., 2006, no. 1, 78–81 | MR | Zbl

[5] Yu. A. Konyaev, D. M. Mikhailov, E. Yu. Romanova, “Asimptoticheskii analiz odnoi giroskopicheskoi sistemy”, Differents. uravneniya, 49:6 (2013), 789–793 | MR | Zbl

[6] Yu. A. Konyaev, Nguen Vet Khoa, “Spektralnyi analiz nekotorykh klassov neavtonomnykh sistem s periodicheskoi i polinomialno periodicheskoi matritsami”, Vestn. Nats. issled. yad. un-ta MIFI, 3:3 (2014), 290–296

[7] A. P. Kartashev, B. L. Rozhdestvenskii, Obyknovennye differentsialnye uravneniya i osnovy variatsionnogo ischisleniya, Nauka, M., 1980 | MR | Zbl