Geodesic
The existence of a~solution of an equation of infinite order with a~given type of growth
Matematičeskie zametki, Tome 13 (1973) no. 5, pp. 677-686.

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In this paper we establish the existence of a particular solution for an equation of infinite order with constant coefficients belonging to a certain class of either infinitely differentiable on the real axis, or entirely analytic, functions. 
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     author = {Yu. F. Korobeinik},
     title = {The existence of a~solution of an equation of infinite order with a~given type of growth},
     journal = {Matemati\v{c}eskie zametki},
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Yu. F. Korobeinik. The existence of a~solution of an equation of infinite order with a~given type of growth. Matematičeskie zametki, Tome 13 (1973) no. 5, pp. 677-686. http://geodesic.mathdoc.fr/item/MZM_1973_13_5_a5/