一类微分差分方程的整函数解  

Entire Solutions to a Certain Type of Differential-difference Equations

作　　者：吴丽镐 张然然 黄志波[3] Li Hao WU;Ran Ran ZHANG;Zhi Bo HUANG(School of Computer Engineering,Gungzhou College of South China University of Technology,Guangzhou 510800,P.R.China;Department of Mathematics,Guangdong University of Education,Guangzhou 510303,P.R.China;School of Mathematical Sciences,South China Normal University,Guangzhou 510631,P.R.China)

机构地区：[1]华南理工大学广州学院计算机工程学院,广州510800 [2]广东第二师范学院数学系,广州510303 [3]华南师范大学数学科学学院,广州510631

出　　处：《数学学报（中文版）》2021年第3期471-478,共8页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金(11801093,11871260);广东省自然科学基金(2018A030313508);广东省普通高校特色创新类项目(2019KTSCX119);广州市科技计划(202002030228)。

摘　　要：本文考虑一类非线性微分差分方程f(z)n+L(z,f)=q(z)e^(p(z)),其中n≥2为自然数,L(z,f)(■0)是关于f(z)的线性微分差分多项式,p(z)和q(z)是非零多项式在该方程具有超级小于1的超越整函数解的假设下,证明了n=2且λ^(-)(f)=σ(f)=degp(z),并给出二次微分差分方程整函数解的具体表示.We investigate the nonlinear differential-difference equations of form f(z)_(n)+L(z,f)=q(z)e^(p(z)),where n≥2,L(z,f)(■0)is a linear differential-difference polynomial in f(z),with small functions as its coefficients,p(z)and q(z)are non-vanishing polynomials.We first obtain that n=2 and f(z)satisfiesλ^(-)(f)=σ(f)=degp(z)if the equation possesses a transcendental entire solution of hyper orderσ_(2)(f)<1.Furthermore,the exact form of the entire solutions of the equation is also obtained.

关 键 词：微分差分方程 差分方程 整函数解 

分 类 号：O174.5[理学—数学]