一类非线性微分差分方程的指数多项式解  

Exponential Polynomial Solutions of One Class of Non-Linear Differential-Difference Equations

作　　者：韦燕红 陈莉[1] 

机构地区：[1]五邑大学数学与计算科学学院,广东 江门

出　　处：《理论数学》2021年第10期1739-1746,共8页Pure Mathematics

摘　　要：本文研究一类非线性微分差分方程fn(z)+q(z)eQ(z)L(z,f)=p1eα1z+p2eα2z ,且f(z)满足f∈Γ0的有穷级整函数解,得到 或 ,其中B是常数;n≥k+2,n,k是非零整数,L(z,f)是不恒为零的k次齐次线性微分–差分多项式;q(z)是非恒为零多项式,Q(z)是非常数多项式,p1,p2,α1,α2是非零常数且;并给出2个例子说明解的存在性。本文推广了文献6中Chen等人的结果。In this paper, we study entire solutions of finite order of the following type nonlinear differential-difference equations in the complex plane fn(z)+q(z)eQ(z)L(z,f)=p1eα1z+p2eα2z .If f(z) belongs to Γ0, then or , where B is a constant. n≥k+2,n,k are non-zero integers, L(z,f) is a nonvanishing differential-difference polynomial of degree is equal to k.q(z) is a nonvanishing polynomial and Q(z) is not a constant polynomial, p1,p2,α1,α2 are nonzero constants such that . We give two examples, which show the existence of solution. This paper generalizes the results of Chen et al. in literature 6.

关 键 词：值分布 微分差分方程 指数多项式 有穷级 

分 类 号：O17[理学—数学]