Literature cited
Yu. A. Dubinskii, “Sobolev spaces of infinite order and behavior of the solutions of certain boundary-value problems for unbounded growth of the order of equations,” Mat. Sb.,98, No. 2, 163–184 (1975).
Yu. A. Dubinskii, “Nontriviality of Sobolev spaces of infinite order in the case of the complete Euclidean space and the torus,” Mat. Sb.,100, No. 3, 436–446 (1976).
Chan Dyk Van, Nonlinear Differential Equations and Functional Spaces of Infinite Order [in Russian], Belorussian State Univ., Minsk (1983).
A. N. Kolmogorov, “On the inequalities between the suprema of successive derivatives of a function on an infinite interval,” Uch. Zap. Mosk. Gos. Univ., Mat.,30, 3–16 (1939).
A. Gorny, “Contribution a l'étude des fonctions dérivablés d'une variable réelle,” Acta Math.,71, 317–358 (1939).
Yu. A. Dubinskii, “Nontriviality of certain classes of functions and solvability of nonlinear ordinary differential equations of infinite order. II,” Differents. Uravn.,11, No. 7, 1190–1200 (1975).
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Translated from Matematicheskie Zametki, Vol. 39, No. 3, pp. 453–459, March, 1986.
In conclusion, the author expresses deep gratitude to Chan Dyk Van for the formulation of the problem and assistence with the note.
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Bang, K.Z. Nontriviality of the Sobolev-Orlich classes and spaces of infinite order on the line. Mathematical Notes of the Academy of Sciences of the USSR 39, 250–253 (1986). https://doi.org/10.1007/BF01170257
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DOI: https://doi.org/10.1007/BF01170257