Geodesic
Asymptotic behavior of the resolvent of an unstable Volterra equation with kernel depending on the difference of the arguments
Matematičeskie zametki, Tome 62 (1997) no. 1, pp. 88-94.

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We present the structure of the resolvent of a difference kernel, which allows us to study the asymptotic behavior of the solution of the renewal equation for a given asymptotic behavior of the constant term. An asymptotic representation for the resolvent is obtained under minimal requirements on the moments of the kernel. Similar results are given for integro-differential equations. 
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V. A. Derbenev; Z. B. Tsalyuk. Asymptotic behavior of the resolvent of an unstable Volterra equation with kernel depending on the difference of the arguments. Matematičeskie zametki, Tome 62 (1997) no. 1, pp. 88-94. http://geodesic.mathdoc.fr/item/MZM_1997_62_1_a8/

[1] Viner N., Peli R., Preobrazovanie Fure v kompleksnoi oblasti, Nauka, M., 1964

[2] Smith W. L., “Asymptotic renewal theorems”, Proc. Roy. Soc. Edinburgh. Sect. A, 64 (1954), 9–48 | MR | Zbl

[3] Feller V., Vvedenie v teoriyu veroyatnostei i ee prilozheniya, Mir, M., 1984

[4] Sevastyanov B. A., Vetvyaschiesya protsessy, Nauka, M., 1971 | Zbl

[5] Tsalyuk Z. B., “Ob asimptotike reshenii uravneniya vosstanovleniya”, Differents. uravneniya, 6:6 (1970), 1112–1114 | MR | Zbl

[6] Tsalyuk Z. B., “Asimptoticheskie otsenki reshenii uravneniya vosstanovleniya”, Differents. uravneniya, 25:2 (1989), 320–325 | MR

[7] Derbenev V. A., “K voprosu ob asimptotike uravneniya vosstanovleniya”, Differents. uravneniya, 12:4 (1976), 743–746 | MR | Zbl

[8] Levin I. I., Shea D. F., “On the asymptotic behavior of the bounded solutions of some integral equations”, J. Math. Anal. Appl., 37 (1972), 42–82, 288–326, 537–575 | DOI | MR | Zbl

[9] Derbenev V. A., “Asimptotika resheniya neustoichivogo uravneniya vosstanovleniya”, Izv. vuzov. Matem., Kazan, 1976 | Zbl

[10] Derbenev V. A., “Asimptoticheskie svoistva resheniya uravneniya vosstanovleniya”, Matem. analiz, no. 2, Krasnodar, 1974, 43–49 | MR

[11] Derbenev V. A., Tsalyuk Z. B., “K voprosu ob asimptoticheskom razlozhenii reshenii uravneniya vosstanovleniya”, Differents. uravneniya, 10:4 (1974), 335–341 | MR | Zbl

[12] Tsalyuk Z. B., “O dopustimosti nekotorykh par prostranstv dlya integralnykh operatorov i uravnenii Volterra”, Differents. uravneniya, 13:11 (1977), 2096–2098 | MR | Zbl