Geodesic
On a generalization of Ambartsumyan's equation
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 156 (2014) no. 4, pp. 25-30 Cet article a éte moissonné depuis la source Math-Net.Ru

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The paper discusses the functional-differential equation $$ y'(t)+ay(t)=\sum^n_{j=1}b_jy(\lambda_jt),\qquad t>0, $$ where $a>0$, $b_j\in R$, $\lambda>1$. Such equation arises from a generalization of Ambartsumyan's model of light absorption in the interstellar space. The existence of the solution to this equation, which can be written in the form of a series, is demonstrated.
Keywords: Ambartsumyan's equation, functional-differential equation, recurrence relation, existence theorem. 
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     title = {On a~generalization of {Ambartsumyan's} equation},
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N. P. Evlampiev; A. M. Sidorov; I. E. Philippov. On a generalization of Ambartsumyan's equation. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 156 (2014) no. 4, pp. 25-30. http://geodesic.mathdoc.fr/item/UZKU_2014_156_4_a2/

[1] Evlampiev N. P., Mokeichev V. S., Filippov I. E., “Vyvod uravneniya dlya plotnosti raspredeleniya yarkosti sveta v sluchae razlichnykh oblakov”, Uchen. zap. Kazan. un-ta. Ser. Fiz.-matem. nauki, 154, no. 4, 2012, 126–129

[2] Ambartsumyan V. A., Nauchnye trudy, v 3 t., v. 1, Izd-vo AN Arm. SSR, Erevan, 1960, 430 pp.

[3] Mokeichev V. S., Evlampiev N. P., “O reshenii na poluosi differentsialno-raznostnogo uravneniya”, Izv. vuzov. Matem., 1991, no. 4, 44–47 | MR | Zbl

[4] Kato T., McLeod J. B., “The functional-differential equation $y'(x)=ay(\lambda x)+by(x)$”, Bull. Amer. Math. Soc., 77:6 (1971), 891–937 | DOI | MR | Zbl

[5] Rusakov G. I., “Fluktuatsii yarkosti Mlechnogo puti”, Uchen. zap. Leningr. un-ta. Ser. matem. nauk, 18, 1949, 53–79