On the Malmquist theorem for solutions of differential equations in the neighborhood of an isolated singular point

被引：0

作者：

Mokhon'ko A.A. ^{[1
]}

机构：

[1] Shevchenko Kiev National University, Kiev

来源：

Ukrainian Mathematical Journal | 2005年 / 57卷 / 4期

关键词：

Differential Equation; Singular Point; Meromorphic Solution; Malmquist Theorem;

D O I：

10.1007/s11253-005-0214-7

中图分类号：

学科分类号：

摘要：

The statement of the Malmquist theorem (1913) about the growth of meromorphic solutions of the differential equation f′ = P(z,f)/Q(z,f), where P(z, f) and Q(z, f) are polynomials in all variables, is proved in the case of solutions with isolated singular point at infinity. © 2005 Springer Science+Business Media, Inc.

引用

页码：610 / 620

页数：10

共 13 条

[1]

Gol'dberg A.A., Ostrovskii I.V., Distribution of Values of Meromorphic Functions [in Russian], Nauka, Moscow, (1970)

[2]

Malmquist J., Sur les fonctions á un nombre fini de branches définies par les équations différentielles du premier ordre, Acta Math., 36, pp. 297-343, (1913)

[3]

Golubev V.V., Lectures on the Analytic Theory of Differential Equations [in Russian], (1950)

[4]

Yosida K., A generalization of a Malmquist's theorem, Jpn. J. Math., 9, pp. 239-256, (1933)

[5]

Gol'dberg A.A., Levin B.Ya., Ostrovskii I.V., Entire and meromorphic functions, VINITI Series in Contemporary Problems of Mathematics, Fundamental Trends [in Russian], 85, pp. 5-186, (1991)

[6]

Laine I., Nevanlinna Theory and Complex Differential Equations, (1993)

[7]

Van Der Waerden B.L., Algebra [Russian Translation], (1979)

[8]

Mokhon'ko A.Z., Malmquist theorem for solutions of differential equations in a neighborhood of a logarithmic singular point, Ukr. Mat. Zh., 56, 4, pp. 476-483, (2004)

[9]

Valiron G., Sur la dérivée des fonctions algébroides, Bull. Soc. Math. France, 59, 1-2, pp. 17-39, (1931)

[10]

Markushevich A.I., Theory of Analytic Functions [in Russian], 2, (1968)

← 1 2 →