两类非线性微分-差分方程的整函数解

doi:10.6040/j.issn.1671-9352.0.2021.785

《山东大学学报(理学版)》 ›› 2022, Vol. 57 ›› Issue (12): 34-44.doi: 10.6040/j.issn.1671-9352.0.2021.785

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两类非线性微分-差分方程的整函数解

高真光

暨南大学信息科学技术学院, 广东广州 510632

发布日期:2022-12-05
作者简介:高真光(1998— ),男,硕士研究生,研究方向为复分析. E-mail:gzg980104@163.com
基金资助:
国家自然科学基金资助项目(12171127)

Entire solutions of two types of nonlinear differential-difference equations

GAO Zhen-guang

College of Information Science and Technology, Jinan University, Guangzhou 510632, Guangdong, China

Published:2022-12-05

摘要/Abstract

摘要： 利用Nevanlinna值分布理论,研究了两类非线性微分-差分方程f ⁿ+ωf ^n-1f '+b(f ')ⁿ+qe^Qf(z+c)=ue^v和f ⁿ+ω₁f ^n-1f '+ω₂(f ')ⁿ+qe^Qf(z+c)=p₁e^λ₁z+p₂e^λ₂z的有限级整函数解的存在性,得到了两个结果,并举例证明文中所得结果是精确的。

关键词: 非线性微分-差分方程, 整函数解, 主次项, 增长级

Abstract: Using Nevanlinna's value distribution theory, this paper investigates the existence of entire solutions with finite order of two types of nonlinear differential-difference equations of the forms f ⁿ+ωf ^n-1f '+b(f ')ⁿ+qe^Qf(z+c)=ue^v and f ⁿ+ω1f ^n-1f '+ω2(f ')ⁿ+qe^Qf(z+c)=p1e^λ1z+p2e^λ2z, and obtains two results. Examples are provided to show that the results obtained in this paper, in a sense, are best possible.

Key words: nonlinear differential-difference equation, entire solution, dominant term, order of growth

中图分类号:

O174.52

高真光. 两类非线性微分-差分方程的整函数解[J]. 《山东大学学报(理学版)》, 2022, 57(12): 34-44.

GAO Zhen-guang. Entire solutions of two types of nonlinear differential-difference equations[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2022, 57(12): 34-44.

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两类非线性微分-差分方程的整函数解

Entire solutions of two types of nonlinear differential-difference equations

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