References
Bank, S., Kaufman, R.: On meromorphic solutions of first-order differential equations. Comment. Math. Helvetici51, 289–299 (1976)
Bank, S., Kaufman, R.: On the Weierstrass functions, Sigma, Zeta, Pe, and their functional and differential equations. Aequationes Math.16, 149–164 (1977)
Bieberbach, L.: Theorie der gewöhnlichen Differentialgleichungen, 2. Aufl., b. 66. Berlin, Heidelberg, New York: Springer 1965
Gackstatter, F., Laine, I.: Zur Theorie der gewöhnlichen Differentialgleichungen im Komplexen (to appear)
Gol'dberg, A.: On single-valued solutions of first-order differential equations. Ukrain. Mat. Z.8, 254–261 (1956) (Russian)
Hayman, W.: Meromorphic functions. Oxford Math. Monographs. Oxford: Clarendon Press 1964
Hille, E.: On some generalizations of the Malmquist theorem. Math. Scand.39, 59–79 (1976)
Hille, E.: Ordinary differential equations in the complex domain. New York: Wiley-Interscience 1976
Laine, I.: On the behavior of the solutions of some first-order differential equations. Ann. Acad. Sci. Fenn., Ser. A, I497, 26 (1971)
Laine, I.: Admissible solutions of some generalized algebraic differential equations. Publ. Univ. Joensuu, Ser. B10, 6 (1974)
Malmquist, J.: Sur les fonctions à un nombre fini des branches définies par les équations différentielles du premier ordre. Acta Math.36, 297–343 (1913)
Nevanlinna, R.: Le théorème de Picard-Borel et la théorie des fonctions méromorphes. Paris: Gauthier-Villars 1929
Saks, S., Zygmund, A.: Analytic functions. Monografie Mat., Tom 28 (Engl. transl.). Warsaw 1952
Strelitz, Sh.: A remark on meromorphic solutions of differential equations. Proc. Amer. Math. Soc.65, 255–261 (1977)
Strelitz, Sh.: Asymptotic properties of analytic solutions of differential equations. Vilnius 1972 (Russian)
Valiron, G.: Lectures on the general theory of integral functions. Toulouse: Edouard Privat 1923
Wittich, H.: Zur Theorie der Riccatischen Differentialgleichung. Math. Ann.127, 433–450 (1954)
Wittich, H.: Einige Eigenschaften der Lösungen vonw′ = a(z) + b(z)w + c(z)w 2. Arch. Math.5, 226–232 (1954)
Wittich, H.: Neuere Untersuchungen über eindeutige analytische Funktionen. Ergebnisse der Mathematik, Heft 8. Berlin, Göttingen, Heidelberg: Springer 1955
Wittich, H.: Eindeutige Lösungen der Differentialgleichungw′ = R(z, w). Math. Zeit.74, 278–288 (1960)
Yosida, K.: A generalization of a Malmquist's theorem. Japan J. Math.9, 253–256 (1933)
Author information
Authors and Affiliations
Additional information
The research of both authors was supported in part by the National Science Foundation. (For the first author, Grant Nos. MCS 76-07214 and MCS 78-02188. For the second author, Grant No. MCS 76-07471)
Rights and permissions
About this article
Cite this article
Bank, S.B., Kaufman, R.P. On the order of growth of meromorphic solutions of first-order differential equations. Math. Ann. 241, 57–67 (1979). https://doi.org/10.1007/BF01406708
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01406708