Geodesic
Sign-definiteness of solutions and stability of linear differential equations with variable distributed delay
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 8 (2008), pp. 73-77 Cet article a éte moissonné depuis la source Math-Net.Ru

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We study one class of linear differential equations with varying distributed delay. We obtain an effective (in terms of parameters of the initial problem) criterion for the positiveness of the Cauchy function of this class of equations. On the base of this result we establish effective criteria for the exponential stability of equations under consideration.
Keywords: equations with delay, exponential stability, Cauchy function.
Mots-clés : nonoscillation 
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     title = {Sign-definiteness of solutions and stability of linear differential equations with variable distributed delay},
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V. V. Malygina; T. L. Sabatulina. Sign-definiteness of solutions and stability of linear differential equations with variable distributed delay. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 8 (2008), pp. 73-77. http://geodesic.mathdoc.fr/item/IVM_2008_8_a7/

[1] Azbelev N. V., Maksimov V. P., Rakhmatullina L. F., Vvedenie v teoriyu funktsionalno-differentsialnykh uravnenii, Nauka, M., 1991, 280 pp. | MR | Zbl

[2] Azbelev N. V., Simonov P. M., Ustoichivost uravnenii s obyknovennymi proizvodnymi, Izd-vo Permsk. un-ta, Perm, 2001, 230 pp. | MR

[3] Malygina V. V., “Positiveness of the Cauchy function and stability of a linear differential equation with distributed delay”, Memoirs on Diff. Equat. Math. Phys., 41 (2007), 87–96 | MR | Zbl

[4] Gusarenko S. A., Domoshnitskii A. I., “Ob asimptoticheskikh i ostsillyatsionnykh svoistvakh lineinykh skalyarnykh funktsionalno-differentsialnykh uravnenii pervogo poryadka”, Differents. uravneniya, 25:12 (1989), 2090–2103 | MR | Zbl

[5] Sugie J., “Oscillation solutions of scalar delay-differential equations with state dependence”, Appl. Anal., 27 (1988), 217–227 | DOI | MR | Zbl

[6] Burton T. A., Hatvani L., “On nonuniform asymptotic stability for nonautonomous functional differential equations”, Diff. Integral Equat., 3:2 (1990), 285–293 | MR | Zbl

[7] Scheglov V. A., “Ustoichivost lineinogo differentsialnogo uravneniya s raspredelennym zapazdyvaniem”, Differents. uravneniya, 32:12 (1996), 1665–1669 | MR

[8] Vagina M. Yu., “Logisticheskaya model s zapazdyvayuschim usredneniem”, Avtomatika i telemekhanika, 2003, no. 4, 167–173 | MR | Zbl

[9] Funacubo M., Hara T., Sakata S., “On the uniform asymptotic stability for a linear integro-differential equation of Volterra type”, J. Math. Anal. Appl., 324 (2006), 1036–1049 | DOI | MR

[10] Sabatulina T. L., Malygina V. V., “Nekotorye priznaki ustoichivosti lineinykh avtonomnykh differentsialnykh uravnenii s raspredelennym zapazdyvaniem”, Izv. vuzov. Matematika, 2007, no. 6, 55–63 | MR