Geodesic
Approximating characteristic equations for autonomous systems of differential equations with aftereffect
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 1 (2011), pp. 10-23.

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In this paper we construct approximating polynomial characteristic equations for a linear autonomous system with aftereffect. The procedures for constructing approximating characteristic equations use analytic representations of resolvents of infinitesimal operators and the theory of characteristic determinants and perturbation determinants in a separable Hilbert space.
Keywords: differential equation with aftereffect, infinitesimal operators, resolvent, characteristic equation, approximation, characteristic determinant
Mots-clés : perturbation determinant. 
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D. S. Bykov; Yu. F. Dolgii. Approximating characteristic equations for autonomous systems of differential equations with aftereffect. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 1 (2011), pp. 10-23. http://geodesic.mathdoc.fr/item/IVM_2011_1_a1/

[1] Krasovskii N. N., Nekotorye zadachi teorii ustoichivosti dvizheniya, Fizmatgiz, M., 1959 | MR

[2] Dolgii Yu. F., “Asimptotika kharakteristicheskikh pokazatelei funktsionalno-differentsialnykh uravnenii”, Izv. Uralsk. gos. un-ta, 46:10 (2006), 50–59 | Zbl

[3] Meiman N. N., Chebotarev N. G., “Problema Rausa–Gurvitsa dlya polinomov i tselykh funktsii”, Tr. Matem. in-ta im. V. A. Steklova, 26, 1949, 3–332 | MR

[4] Pontryagin L. S., “O nulyakh nekotorykh elementarnykh transtsendentnykh funktsii”, Izv. AN SSSR. Ser. matem., 6:3 (1942), 115–134 | MR | Zbl

[5] Andreichikov I. P., Yudovich V. I., “Ob ustoichivosti vyazkouprugikh sterzhnei”, Izv. AN SSSR. Mekhanika tverdogo tela, 1974, no. 2, 78–87

[6] Fabiano R. H., “Stability and approximation for a linear viscoelastic model”, J. Math. Analys. Appl., 204:1 (1996), 206–220 | DOI | MR | Zbl

[7] Krasovskii N. N., “Ob approksimatsii odnoi zadachi analiticheskogo konstruirovaniya regulyatorov v sisteme s zapazdyvaniem”, PMM, 28:4 (1964), 716–724 | MR

[8] Osipov Yu. S., “O stabilizatsii upravlyaemykh sistem s zapazdyvaniem”, Differents. uravneniya, 1:5 (1965), 605–618 | MR | Zbl

[9] Markushin E. M., Shimanov S. N., “Priblizhennoe reshenie zadachi analiticheskogo konstruirovaniya regulyatora dlya uravneniya s zapazdyvaniem”, Differents. uravneniya, 2:8 (1966), 1018–1026 | Zbl

[10] Gokhberg I. Ts., Krein M. G., Vvedenie v teoriyu lineinykh nesamosopryazhennykh operatorov v gilbertovom prostranstve, Nauka, M., 1965, 448 pp. | MR

[11] Fikhtengolts G. M., Kurs differentsialnogo i integralnogo ischisleniya, v. 2, Nauka, M., 1969, 656 pp.

[12] Polia G., Sege G., Zadachi i teoremy iz analiza, v. 1, Nauka, M., 1978

[13] Akhiezer N. I., Glazman I. M., Teoriya lineinykh operatorov v gilbertovom prostranstve, Nauka, M., 1966, 544 pp. | MR | Zbl