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

摘要: 本文研究一类非线性微分差分方程fⁿ(z)+q(z)e^Q(z)L(z,f)=p₁e^α₁z+p₂e^α₂z ，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。

Abstract: 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)e^Q(z)L(z,f)=p₁e^α₁z+p₂e^α₂z .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.