Abstract

For some large classes of differential equations of the first order we give bounds for Ahlfors-Shimizu characteristics of meromorphic solutions in the complex plane of these equations. The considered equations largely generalize algebraic ones for which the obtained results imply the known Goldberg theorem. Characteristics of meromorphic solutions in a given domain weren’t studied at al. We consider solutions in a given domain of some (large) equations and give bounds for Ahlfors–Shimizu characteristic for these solutions.

中文翻译：

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一阶非代数方程组解的一些估计

摘要

对于一类大型的一阶微分方程，我们给出了这些方程的复平面中亚纯解的Ahlfors-Shimizu特征的界限。所考虑的方程式在很大程度上概括了代数方程式，对于这些方程式，所得结果暗示了已知的Goldberg定理。尚未研究给定域中亚纯解的特征。我们考虑某些（大型）方程的给定域中的解，并为这些解给出Ahlfors–Shimizu特征的界限。