论某些费马型函数方程的同态解

Pub Date : 2024-07-09 DOI:10.3103/s1068362324700092

J. T. Lu, J. F. Xu

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引用次数: 0

摘要

摘要本文研究了函数方程 \(f(z)^{2}+f(z+c)^{3}=e^{P}、f(z)^{2}+f(z+c)^{4}=e^{P}\)和费马方程的差分类似形式 \(f(z)^{3}+[c_{1}f(z+c)+c_{0}f(z)]^{3}=e^{P}\)的解，其中 \(P\) 是多项式。这些结果概括了 Lü 和 Guo [Mediterr.

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On Meromorphic Solutions of Some Fermat-Type Functional Equations

Abstract

In this paper, we study the existence of meromorphic solutions of hyperorder strictly less than 1 to functional equation \(f(z)^{2}+f(z+c)^{3}=e^{P},f(z)^{2}+f(z+c)^{4}=e^{P}\) and the solution of the difference analogue of Fermat-type equation of the form \(f(z)^{3}+[c_{1}f(z+c)+c_{0}f(z)]^{3}=e^{P}\), where \(P\) is a polynomial. These results generalize the results of Lü and Guo [Mediterr. J. Math. 2022] and Ahamed [J. Contemp. Math. Anal. 2021].

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