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Transactions of the American Mathematical Society

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On meromorphic solutions of algebraic differential equations


Author: Sh. Strelitz
Journal: Trans. Amer. Math. Soc. 258 (1980), 431-440
MSC: Primary 34A20; Secondary 30D30
DOI: https://doi.org/10.1090/S0002-9947-1980-0558182-9
MathSciNet review: 558182
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Abstract: The Malmquist Theorem is generalized for equations of the type $ R(z,\,w,\,w',\, \ldots \,,\,{w^{(n)}})\, = \,{{P(z,\,w)}/{Q(z,\,w)}}$ where P, Q and R are polynomials of w and $ w,\,w',\, \ldots \,,\,{w^{(n)}}$ respectively with meromorphic coefficients of finite order.


References [Enhancements On Off] (What's this?)

  • [1] B. Ja. Levin, Distribution of zeros of entire functions, GITTL, Moscow, 1956; English transl., Transl. Math. Monographs, vol. 5, Amer. Math. Soc., Providence, R. I., 1964. MR 19, 402; MR 28 #217. MR 0156975 (28:217)
  • [2] I. Malmquist, Sur les fonctions à un nombre fini de branches définies par les equations differentielles du premier ordre, Acta Math. 36 (1913), 297-343. MR 1555091
  • [3] Sh. Strelitz, Asymptotic properties of analytic solutions of differential equations, ``Mintis", Vilnius, 1972. (Russian) MR 0499384 (58:17268)
  • [4] -, A remark on meromorphic solutions of algebraic differential equations, Proc. Amer. Math. Soc. 65 (1977), 255-261. MR 0486726 (58:6427)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1980-0558182-9
Keywords: Meromorphic functions, algebraic differential equations
Article copyright: © Copyright 1980 American Mathematical Society

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