Scholarlink

<p>In this paper, we focus on exploring entire solutions of finite order for a class of differential-difference equations, particularly those of the following form</p><p><Equation ID="Equa"> <EquationSource Format="TEX">\(\begin{cases}w_1'(z)^2+{P_2^2}(z)w_2{(z+c)^2} = Q_1(z),\\w_2'(z)^2+{P_1^2}(z)w_1{(z+c)^2} = Q_2(z),\end{cases}\)</EquationSource> </Equation></p><p>where <i>P</i><sub><i>i</i></sub>, <i>Q</i><sub><i>i</i></sub> (<i>i</i> = 1, 2) are non-zero polynomials. We prove that the above system admits four distinct forms of solutions and derive their specific expressions. Additionally, we establish the relationship between the coefficients of the system and those of its solutions. These results extend the existing results of complex differential (difference) equations to the systems of differential-difference equations, and improve the current results related to the systems of differential-difference equations.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

On entire solutions of some types of systems of complex differential-difference equations

  • 期刊论文

  • 发表日期：

    2026年8月5日

查看全文
  • Chuangxin Chen,
  • Ranran Zhang,
  • Zongxuan Chen

摘要

In this paper, we focus on exploring entire solutions of finite order for a class of differential-difference equations, particularly those of the following form

\(\begin{cases}w_1'(z)^2+{P_2^2}(z)w_2{(z+c)^2} = Q_1(z),\\w_2'(z)^2+{P_1^2}(z)w_1{(z+c)^2} = Q_2(z),\end{cases}\)

where Pi, Qi (i = 1, 2) are non-zero polynomials. We prove that the above system admits four distinct forms of solutions and derive their specific expressions. Additionally, we establish the relationship between the coefficients of the system and those of its solutions. These results extend the existing results of complex differential (difference) equations to the systems of differential-difference equations, and improve the current results related to the systems of differential-difference equations.