一类非线性复微分差分方程解的不存在性

数学物理学报 ›› 2021, Vol. 41 ›› Issue (1): 69-80.

一类非线性复微分差分方程解的不存在性

林书情(),陈俊凡*()

福建师范大学数学与信息学院 & 福建省分析数学及应用重点实验室福州 350117

收稿日期:2020-02-14 出版日期:2021-02-26 发布日期:2021-01-29
通讯作者: 陈俊凡 E-mail:shuqinglin1996@163.com;junfanchen@163.com
作者简介:林书情, E-mail: shuqinglin1996@163.com
基金资助:
国家自然科学基金(11301076);福建省自然科学基金(2018J01658);福建省自然科学基金(2019J01672)

The Non-Existence of Solutions of a Certain type of Nonlinear Complex Differential-Difference Equations

Shuqing Lin(),Junfan Chen*()

College of Mathematics and Informatics & Fujian Key Laboratory of Mathematical Analysis and Applications, Fujian Normal University, Fuzhou 350117

Received:2020-02-14 Online:2021-02-26 Published:2021-01-29
Contact: Junfan Chen E-mail:shuqinglin1996@163.com;junfanchen@163.com
Supported by:
Supported by the NSFC(11301076);the NSF of Fujian Province(2018J01658);the NSF of Fujian Province(2019J01672)

摘要/Abstract

摘要：

该文研究了一类复微分差分方程 $ \left[f(z)f'(z)\right]^{n}+f^{m}(z+\eta)=1，\nonumber $ $ \left[f(z)f'(z)\right]^{n}+[f(z+\eta)-f(z)]^{m}=1， $ $\left[f(z)f'(z)\right]^{2}+P^{2}(z)f^{2}(z+\eta)=Q(z)e^{\alpha(z)} $ 的超越整函数解，其中 $P(z)， $ $ Q(z)$为非零多项式， $\alpha(z) $为多项式， $ m，$ $ n$为正整数， $\eta\in{\Bbb C}\setminus\{0\} $，并给出了这类方程不存在超越整函数解的几个充分条件.

关键词: 复微分差分方程, 超越整函数解, Nevanlinna理论, 有穷级

Abstract:

In this paper, we study transcendental entire solutions of a certain type of complex differential-difference equations $\left[f(z)f'(z)\right]^{n}+f^{m}(z+\eta)=1,$ $\left[f(z)f'(z)\right]^{n}+[f(z+\eta)-f(z)]^{m}=1,$ $\left[f(z)f'(z)\right]^{2}+P^{2}(z)f^{2}(z+\eta)=Q(z)e^{\alpha(z)},$ where $P(z) $ and $Q(z) $ are non-zero polynomials, $\alpha(z) $ is polynomial, $ m$ and $n $ are positive integers, $ \eta\in{\Bbb C}\setminus\{0\}$. Several sufficient conditions on the non-existence of transcendental entire solutions of such equations are supplied.

Key words: Complex differential difference equation, Transcendental entire solution, Nevanlinna theory, Finite order

中图分类号:

O174.52

林书情,陈俊凡. 一类非线性复微分差分方程解的不存在性[J]. 数学物理学报, 2021, 41(1): 69-80.

Shuqing Lin,Junfan Chen. The Non-Existence of Solutions of a Certain type of Nonlinear Complex Differential-Difference Equations[J]. Acta mathematica scientia,Series A, 2021, 41(1): 69-80.

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