Geodesic
Stability tests for the solutions of linear operator equations with discrete and continuous lags in the arguments
Izvestiya. Mathematics , Tome 4 (1970) no. 2, pp. 465-477.

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Necessary and sufficient criteria are established for the exponential growth (in particular, boundedness) of the solutions of equations (1)–(2). The results obtained generalize the contents of $({}^1)$. 
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Z. I. Rekhlitskii. Stability tests for the solutions of linear operator equations with discrete and continuous lags in the arguments. Izvestiya. Mathematics , Tome 4 (1970) no. 2, pp. 465-477. http://geodesic.mathdoc.fr/item/IM2_1970_4_2_a10/

[1] Rekhlitskii Z. I., “Ob ustoichivosti reshenii nekotorykh operatornykh uravnenii s zapazdyvayuschimi argumentami”, Izv. AN SSSR. Ser. matem., 31 (1967), 391–400