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Petrenko, V. P.

Growth of algebroid solutions of algebraic differential equations. (English. Russian original) Zbl 0456.30028

Sib. Math. J. 21, 628-637 (1981); translation from Sib. Mat. Zh. 21, No. 4, 194-205 (1980).
See the review of the Russian original in Zbl 0436.30025.
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scan of Zbl 0456.30028

MSC:

30D35 Value distribution of meromorphic functions of one complex variable, Nevanlinna theory
30D99 Entire and meromorphic functions of one complex variable, and related topics
34M99 Ordinary differential equations in the complex domain

Keywords:

algebraic differential equations with meromorphic coefficients; growth of algebroid functions; value distribution theory

Citations:

Zbl 0436.30025; Zbl 0194.11101
Cite Review PDF
Full Text: DOI

References:

[1] G. Valiron, ?Sur la dérivee des fonctions algebroides,? Bull. Soc. Math. France,59, Nos. 1 and 2, 17-39 (1931). · JFM 57.0371.01
[2] H. Selberg, ?Über die Wertverteilung der algebroiden Funktionen,? Math. Z.,31, 709-729 (1930). · JFM 56.0280.06 · doi:10.1007/BF01246442
[3] H. Cartan, ?Sur les zèros des combinaisons lineaires des p-functions holomorphes,? Mathematica (cluj),7, 5-31 (1933). · Zbl 0007.41503
[4] V. P. Petrenko, ?The distribution of values of certain entire functions of several variables,? Dokl. Akad. Nauk SSSR,223, No. 1, 46-48 (1975). · Zbl 0324.32005
[5] H. Weil, Meromorphic Functions and Analytic Curves, Princeton Univ. Press (1943). · Zbl 0061.15302
[6] A. A. Gol’dberg, Questions in the Theory of Value Distributions. Supplement to G. Vittikh’s book ?Contemporary Investigations of Single-Valued Analytic Functions,? [in Russian], Fizmatgiz, Moscow (1960).
[7] V. P. Petrenko and M. Hussein, ?The growth of entire functions,? Izv. Akad. Nauk SSSR, Ser. Mat.,37, No. 2, 466-477 (1973).
[8] V. P. Petrenko, ?Relations between G. Valiron’s deviations and defects for entire curves and variable multivectors,? Izv. Akad. Nauk SSSR, Ser. Mat.,40, No. 2, 326-337 (1976).
[9] U. Heyman, Meromorphic Functions [Russian translation], Mir, Moscow (1966).
[10] V. D. Mokhon’ko, ?A lemma concerning the logarithmic derivative for algebroid functions,? in: The Theory of Functions, Fucntional Analysis, and Their Applications [in Russian], Vol. 20, Kharkov (1974), pp. 112-122.
[11] G. Vittikh, Contemporary Investigations of Single-Valued Analytic Functions [in Russian], Fizmatgiz, Moscow (1960).
[12] G. Valiron, Analytic Functions [Russian translation], Gostekhizdat, Moscow (1957).
[13] Sh. I. Strelits, Asymptotic Properties of Analytic Solutions of Differential Equations [in Russian], Mintas, Vilnus (1972). · Zbl 0235.34080
[14] A. Z. Mokhon’ko and V. D. Mokhon’ko, ?Investigation of Nevanlinna characteristics of certain meromorphic functions and their application to differential equations,? Sib. Mat. Zh.,15, No. 6, 1305-1332 (1974).
[15] S. S. Boiko and V. P. Petrenko, ?Asymptotic properties of solutions of linear differential equations with entire coefficients,? Dokl. Akad. Nauk Ukr. SSR, Ser. A, No. 2, 99-102 (1977). · Zbl 0349.34003
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