Geodesic
On the question of the theorem of Bohl --- Perron of hybrid linear functional differential systems with aftereffect (HLFDSA)
Žurnal Srednevolžskogo matematičeskogo obŝestva, Tome 18 (2016) no. 1, pp. 75-81.

Voir la notice de l'article provenant de la source Math-Net.Ru

The abstract hybrid system of functional differential equations is given. One part of the equation for variable functional differential, according to another of the variables is the difference one, the second part of the equation for variable differential, according to another of the variables is functional differential one. There is a system of two equations with two unknowns. Apply W-method N.V. Azbelev’s to two equations. Two model equations were studied: one is a system of functional differential equations, and the second is a system of differential equations. We studied the solutions spaces. Received Bohl – Perron theorem's for the exponential stability of the hybrid system of functional differential equations.
Keywords: theorem of Bohl – Perron, hybrid linear system of functional differential equations, stability, model equations' method. 
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P. M. Simonov. On the question of the theorem of Bohl --- Perron of hybrid linear functional differential systems with aftereffect (HLFDSA). Žurnal Srednevolžskogo matematičeskogo obŝestva, Tome 18 (2016) no. 1, pp. 75-81. http://geodesic.mathdoc.fr/item/SVMO_2016_18_1_a8/

[1] V. M. Marchenko, Zh. Zh. Luazo, “Ob ustoichivosti gibridnykh differentsialno-raznostnykh sistem”, Differents. uravneniya, 45:5 (2009), 728–740 | MR | Zbl

[2] A. S. Larionov, P. M. Simonov, “Ustoichivost gibridnykh funktsionalno-differentsialnykh sistem s posledeistviem (GFDSP)”, Vestnik RAEN, 13:4, Temat. nomer “Differentsialnye uravneniya” (2013), 34–37

[3] A. S. Larionov, P. M. Simonov, “Ustoichivost gibridnykh funktsionalno-differentsialnykh sistem s posledeistviem (GFDSP). II”, Vestnik RAEN, 14:5, Temat. nomer “Differentsialnye uravneniya” (2014), 38–45

[4] A. S. Larionov, P. M. Simonov, “Ustoichivost gibridnykh funktsionalno-differentsialnykh sistem s posledeistviem (GFDSP). III”, Vestnik RAEN, 15:3, Temat. nomer “Differentsialnye uravneniya” (2015), 63–69

[5] N. V. Azbelev, P. M. Simonov, Ustoichivost reshenii uravnenii s obyknovennymi proizvodnymi, Perm. un-t, Perm, 2001, 230 pp.

[6] N. V. Azbelev, L. M. Berezanskii, P. M. Simonov, A. V. Chistyakov, “Ustoichivost lineinykh sistem s posledeistviem. II”, Differents. uravneniya, 27:4 (1991), 555–562 | MR | Zbl

[7] N. V. Azbelev, L. M. Berezanskii, P. M. Simonov, A. V. Chistyakov, “Ustoichivost lineinykh sistem s posledeistviem. III”, Differents. uravneniya, 27:10 (1991), 1659–1668 | MR

[8] N. V. Azbelev, L. M. Berezanskii, P. M. Simonov, A. V. Chistyakov, “Ustoichivost lineinykh sistem s posledeistviem. IV”, Differents. uravneniya, 29:2 (1993), 196–204 | MR | Zbl

[9] E. A Barbashin, Vvedenie v teoriyu ustoichivosti, Nauka, M., 1967, 224 pp. | MR

[10] Kh. L Massera, Kh. Kh. Sheffer, Lineinye differentsialnye uravneniya i funktsionalnye prostranstva, Mir, M., 1970, 456 pp. | MR

[11] L. V Kantorovich, G. P. Akilov, Funktsionalnyi analiz, 4-e izd., ispr., Nevskii Dialekt, BKhV-Peterburg, SPb., 2004, 816 pp. | MR