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JOURNALS // Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki // Archive

Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, 2014 Volume 156, Book 4, Pages 25–30 (Mi uzku1277)

This article is cited in 3 papers

On a generalization of Ambartsumyan's equation

N. P. Evlampieva, A. M. Sidorovb, I. E. Philippovc

a "Intek plyus", Kazan, Russia
b Institute of Computer Mathematics and Information Technologies, Kazan (Volga Region) Federal University, Kazan, Russia
c Institute of Computer Mathematics and Information Technologies, Kazan (Volga Region) Federal University, Kazan, Russia

Abstract: 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.

UDC: 517.929

Received: 23.07.2014



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