This paper relates to a recent trend in complex differential equations which studies solutions in a given domain. The classical settings in complex equations were widely studied for meromorphic solutions in the complex plane. For functions in the complex plane, we have a lot of results of general nature, in particular, the classical value distributions theory describing numbers of a-points. Many of these results do not work for functions in a given domain. A recent principle of derivatives permits us to study the numbers of Ahlfors simple islands for functions in a given domain; the islands play, to some extend, a role similar to that of the numbers of simple a-points. In this paper, we consider a large class of higher order differential equations admitting meromorphic solutions in a given domain. Applying the principle of derivatives, we get the upper bounds for the numbers of Ahlfors simple islands of similar solutions.

中文翻译：

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关于在给定域中允许亚纯解的一些高阶方程

本文涉及研究给定域中解的复杂微分方程的最新趋势。复杂方程中的经典设置被广泛研究用于复平面中的亚纯解。对于复平面中的函数，我们有很多一般性质的结果，特别是描述 a 点数量的经典值分布理论。许多这些结果不适用于给定域中的函数。最近的导数原理允许我们研究给定域中函数的 Ahlfors 简单岛的数量；在某种程度上，这些岛的作用类似于简单 a 点的数量。在本文中，我们考虑在给定域中允许亚纯解的一大类高阶微分方程。应用导数原理，