涉及线性微分不等式的亚纯函数族的拟正规定则

Quasi-normal Criterion for Families of Meromorphic Functions Involving Linear Differential Inequalities

摘要

利用Montel定则,结合微分方程相关理论,研究一类三阶常系数线性微分不等式亚纯函数的拟正规定则及拟正规的阶数,结果表明, $\forall f \in \mathscr{F}$,当$\left|f^{\prime \prime \prime}(z)+A f(z)\right|>C$且$\mathscr{F}_{1}=\left\{f^{\prime}(z) / f(z) \mid f(z) \in \mathscr{F}^{\prime}\right\}$或$\mathscr{F}_{2}=\left\{f^{\prime \prime \prime}(z) / f(z) \mid f(z) \in \mathscr{F}\right\}$正规时,亚纯函数族F拟正规.

Abstract

By using Montel’s criterion and combining it with relevant theories of differential equations, we studied the quasi-normal criterion and the order of quasi-normality for a class of meromorphic functions satisfying third-order linear differential inequalities with constant coefficients. The results show that for all f $\in \mathscr{F}$, when $\left|f^{\prime \prime \prime}(z)+A f(z)\right|>C $and $\mathscr{F}_{1}=\left\{f^{\prime}(z) / f(z) \mid f(z) \in \mathscr{F}\right\}$ or $\mathscr{F}_{2}=\left\{f^{\prime \prime \prime}(z) / f(z)|f(z)| \in \mathscr{F}\right\}$ is normal, the family F of meromorphic functions is quasi-normal.

关键词

亚纯函数 / 拟正规族 / 微分不等式 / 正规定则

Key words

meromorphic function / quasi-normal family / differential inequality / normal criterion

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基金资助

新疆维吾尔自治区自然科学基金(2022D01A217)

国家自然科学基金(12061077)