Geodesic
The stability of solutions of certain operator equations with lagging arguments
Izvestiya. Mathematics , Tome 1 (1967) no. 2, pp. 381-390.

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We consider the equation \begin{gather*} y(t_1,\dots,t_n)-\sum_{q_1\dots q_n}A_{q_1\dots q_n}y(t_1-m^{(1)}_{q_1\dots q_n}a_1,\dots,t_n-m^{(n)}_{q_1\dots q_n}a_n)=f \\ (m^{(k)}_{q_1\dots q_n} \text{ -- are integers} \geqslant0;\ a_k>0;\ 0\leqslant t_1,\dots,t_n\infty), \end{gather*} where the $A_{q_1\dots q_n}=A_{q_1\dots q_n}(t_1,\dots,t_n)$ are continuous linear operator-functions operating in a complex Banach space. We establish necessary and sufficient tests for the boundedness of the solutions $y(t_1,\dots,t_n)$ of these equations for all bounded right-hand sides $f=f(t_1,\dots,t_n)$ 
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     title = {The stability of solutions of certain operator equations with lagging arguments},
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Z. I. Rekhlitskii. The stability of solutions of certain operator equations with lagging arguments. Izvestiya. Mathematics , Tome 1 (1967) no. 2, pp. 381-390. http://geodesic.mathdoc.fr/item/IM2_1967_1_2_a10/

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