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On meromorphic solutions of non‐linear differential equations of Tumura–Clunie type
Mathematische Nachrichten ( IF 0.8 ) Pub Date : 2021-02-16 , DOI: 10.1002/mana.201900120 J. Heittokangas 1 , Z. Latreuch 2 , J. Wang 3 , M. A. Zemirni 1
Mathematische Nachrichten ( IF 0.8 ) Pub Date : 2021-02-16 , DOI: 10.1002/mana.201900120 J. Heittokangas 1 , Z. Latreuch 2 , J. Wang 3 , M. A. Zemirni 1
Affiliation
Meromorphic solutions of non‐linear differential equations of the form are investigated, where is an integer, h is a meromorphic function, and is differential polynomial in f and its derivatives with small functions as its coefficients. In the existing literature this equation has been studied in the case when h has the particular form , where are small functions of f and are entire functions. In such a case the order of h is either a positive integer or equal to infinity. In this article it is assumed that h is a meromorphic solution of the linear differential equation with rational coefficients , and hence the order of h is a rational number. Recent results by Liao–Yang–Zhang (2013) and Liao (2015) follow as special cases of the main results.
中文翻译:
Tumura–Clunie型非线性微分方程的亚纯解
形式为非线性微分方程的亚纯解 被调查,在哪里 是整数,h是亚纯函数,并且是f及其微分函数的微分多项式,其系数很小。在现有文献中,当h具有特定形式时已经研究了该方程, 在哪里 是f和的小函数是全部功能。在这种情况下,h的阶为正整数或等于无穷大。在本文中,假设h是线性微分方程的亚纯解 具有合理的系数 ,因此h的阶为有理数。廖扬章(2013)和廖扬(2015)的最新研究结果是主要结果的特例。
更新日期:2021-04-11
中文翻译:
Tumura–Clunie型非线性微分方程的亚纯解
形式为非线性微分方程的亚纯解 被调查,在哪里 是整数,h是亚纯函数,并且是f及其微分函数的微分多项式,其系数很小。在现有文献中,当h具有特定形式时已经研究了该方程, 在哪里 是f和的小函数是全部功能。在这种情况下,h的阶为正整数或等于无穷大。在本文中,假设h是线性微分方程的亚纯解 具有合理的系数 ,因此h的阶为有理数。廖扬章(2013)和廖扬(2015)的最新研究结果是主要结果的特例。