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The existence of a solution of an equation of infinite order with a given type of growth

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Abstract

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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Literature cited

  1. Yu. F. Korobeinik, “Differential equations of infinite order and infinite systems of differential equations,” Izv. Akad. Nauk SSSR, Ser. Mat.,34, No. 4, 881–922 (1970).

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  2. A. O. Gel'fand, The Calculus of Finite Differences [in Russian], Moscow (1952).

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Authors and Affiliations

  1. Rostov State University, USSR

    Yu. F. Korobeinik

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  1. Yu. F. Korobeinik
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Translated from Matematicheskie Zametki, Vol. 13, No. 5, pp. 677–686, May, 1973.

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Korobeinik, Y.F. The existence of a solution of an equation of infinite order with a given type of growth. Mathematical Notes of the Academy of Sciences of the USSR 13, 406–410 (1973). https://doi.org/10.1007/BF01147468

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  • DOI: https://doi.org/10.1007/BF01147468

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