On a generalization of Ambartsumyan's equation

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.