新疆师范大学学报（自然科学版）2024，Vol.43Issue(3)：69-74,6.
Fermat型复微分差分方程的整函数解
Entire Solutions of Fermat Type Complex Differential Difference Equations
摘要
Abstract
This paper investigates the existence of entire solutions of complex differential equations in the form of(μf(z)+λf′(z))2+f(z)2=P(z)and complex differential difference equations in the form of(μf(z)+λf′(z))2+f(z+c)2=P(z)through the complex differential equations theory and the complex difference equations theory.Firstly,the two equations were factored using Weierstrass factorization theorem to compute the specific forms of f(z)and μf(z)+λf′(z);Secondly,the exponent h(z)resulting from the factorization was discussed and divided into two cases,namely,h(z)as a constant and h(z)as a non-constant entire function;Lastly,the relationship between the individual variables in the entire solution was investigated in each of the cases.This article obtains two forms of the existence of entire solutions for Fermat type equations,generalising and improving the previous conclusions from a certain range.关键词
复微分方程/复差分方程/Nevanlinna理论/整函数解Key words
Complex differential equations/Complex difference equations/Nevanlinna theory/Entire solutions分类
数理科学引用本文复制引用
龚翌晖,杨祺..Fermat型复微分差分方程的整函数解[J].新疆师范大学学报（自然科学版）,2024,43(3):69-74,6.基金项目
国家自然科学基金项目(11961068). （11961068）
