Growth properties of meromorphic solutions of some higher-order linear differential-difference equations

Rachid Bellaama, B. Belaïdi
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引用次数: 0

Abstract

Abstract This paper is devoted to the study of the growth of meromorphic solutions of homogeneous and non-homogeneous linear differential-difference equations ∑ i = 0 n ∑ j = 0 m A i ⁢ j ⁢ f ( j ) ⁢ ( z + c i ) = 0 , \displaystyle\sum_{i=0}^{n}\sum_{j=0}^{m}A_{ij}f^{(j)}(z+c_{i})=0, ∑ i = 0 n ∑ j = 0 m A i ⁢ j ⁢ f ( j ) ⁢ ( z + c i ) = F , \displaystyle\sum_{i=0}^{n}\sum_{j=0}^{m}A_{ij}f^{(j)}(z+c_{i})=F, where A i ⁢ j {A_{ij}} ( i = 0 , … , n {i=0,\ldots,n} , j = 0 , … , m {j=0,\ldots,m} ), F are meromorphic functions and c i {c_{i}} ( 0 , … , n {0,\ldots,n} ) are non-zero distinct complex numbers. Under some conditions on the coefficients, we extend early results due to Zhou and Zheng.
一类高阶线性微分-差分方程亚纯解的生长性质
摘要致力于研究亚纯解的增长齐次和非齐次线性差分方程∑i = 0 n∑j = 0 m i⁢j⁢f (j)⁢(z + c i) = 0, \ displaystyle \ sum_ {i = 0} ^ {n} \ sum_ j = {0} ^ {m}现代f ^ {ij} {(j)} (z + c_{我})= 0,∑i = 0 n∑j = 0 m i⁢j⁢f (j)⁢(z + c i) = f \ displaystyle \ sum_ {i = 0} ^ {n} \ sum_ j = {0} ^ {m}现代f ^ {ij} {(j)} (z + c_{我})= f,在那里我⁢j{现代{ij}} (i = 0,…,n {i = 0 \ ldots n}, j = 0,…,m {j = 0, \ ldots m}),F是亚纯函数,ci {c_{i}}(0,…,n {0,\ldots,n})是非零的不同复数。在一定的系数条件下,我们推广了周和郑的早期结果。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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