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A general theorem concerning the growth of solutions of first-order algebraic differential equations. (English) Zbl 0246.34006

MSC:
34M99 Ordinary differential equations in the complex domain
30D35 Value distribution of meromorphic functions of one complex variable, Nevanlinna theory
34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations
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References:
[1] S. Bank [1] On the growth of solutions of algebraic differential equations whose coefficients are arbitrary entire functions , Nagoya Math. J. 39 (1970), 107-117. · Zbl 0201.11502 · doi:10.1017/S0027763000013714
[2] A result concerning meromorphic solutions in the unit disk of algebraic differential equations , Compositio Math. 22 (1970), 367-381. · Zbl 0209.11501 · numdam:CM_1970__22_4_367_0 · eudml:89065
[3] A note on algebraic differential equations whose coefficients are entire functions of finite order . (To appear).
[4] O. Blumenthal [4] Principes de la théorie des fonctions entières d’ordre infini , Gauthier-Villars, Paris, 1910. · JFM 41.0462.01
[5] W. Hayman [5] Picard values of meromorphic functions and their derivatives , Ann. of Math. 70 (1959), 9-42. · Zbl 0088.28505 · doi:10.2307/1969890
[6] R. Nevanlinna [6] Le théorème de Picard-Borel et la théorie des fonctions méromorphes , Gauthier-Villars, Paris, 1929. · JFM 55.0773.03|0357.30019
[7] Analytic functions , Springer-Verlag, New York, 1970 (Engl. Transl.) · Zbl 0199.12501
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[9] M. Tsuji [9] Canonical product for a meromorphic function in a unit circle , J. Math. Soc. Japan 8 (1956), 7-21. · Zbl 0071.28801 · doi:10.2969/jmsj/00810007
[10] G. Valiron [10] Sur les fonctions entières verifiant une classe d’équations différentielles , Bull. Soc. Math. France, 51 (1923), 33-45. · JFM 49.0216.02 · www.numdam.org
[11] Fonctions analytiques et équations différentielles , J. Math. Pures et appl. 31 (1952), 292-303. · Zbl 0047.31003
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