Literature Cited
Yu. A. Dubinskii, “Sobolev spaces of infinite order and the behavior of solutions of certain boundary-value problems when the order of equations increases indefinitely,” Mat. Sb.,98, No. 2, 163–184 (1975).
Yu. A. Dubinskii, “Nonlinear elliptic and parabolic equations,” in: Progress in Science and Technology [in Russian], Contemporary Problems of Mathematics, Vol. 9 (1976), pp. 5–125.
Yu. A. Dubinskii, “On the 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).
Yu. A. Dubinskii, “Nontriviality of Sobolev spaces of infinite order in the case of the whole Euclidean space and the torus,” Mat. Sb.,100, No. 3, 436–446 (1976).
A. Ya. Kobilov, “Nontriviality of certain spaces of infinitely differentiable functions in corner domains and solvability of nonlinear elliptic equations,” Dokl. Akad. Nauk SSSR,266, No. 5, 1040–1044 (1982).
Trân Du'c Vân “Nontriviality of Sobolev-Orlich spaces of infinite order for a bounded domain in the Euclidean space,” Dokl. Akad. Nauk SSSR,250, No. 6, 1331–1334 (1980).
Trân Du'c Vân, “Elliptic equations of infinite order with arbitrary nonlinearities and the corersponding function spaces,” Mat. Sb.,113, No. 2, 245–262 (1980).
W. Rudin, Functional Analysis, McGraw-Hill, New York (1973).
Hà Duy Ban, “On the nontriviality of Sobolev-Orlich classes and spaces of infinite order on the line,” Mat. Zametki,39, No. 3, 453–459 (1986).
Additional information
Hanoi (Vietnam). Translated from Sibirskii Matematicheskii Zhurnal, Vol. 31, No. 1, pp. 208–213, January–February, 1990.
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Ha Duy Bang Criteria for the nontriviality of Sobolev-Orlich classes and spaces of infinite order in the whole Euclidean space. Sib Math J 31, 176–180 (1990). https://doi.org/10.1007/BF00971168
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DOI: https://doi.org/10.1007/BF00971168