Meromorphic solutions of some type of system of differential and difference equations
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摘要: 文章考察了差分方程组 $\begin{eqnarray*}\begin{cases}f_1^n-p_1(z)f_2(z+c)=h_1(z), \ \\f_2^n-p_2(z)f_1(z+c)=h_2(z)\end{cases}\end{eqnarray*}$ 亚纯解的性质,其中n ≥ 4,p1(z)、p2(z)是不为零的多项式,h1(z),h2(z)是整函数.应用值分布理论,得到了该方程组的解是唯一的.此外,文章还讨论了满足一些特殊类微分差分方程构成的方程组存在有限级亚纯解的条件.
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关键词:
- Nevanlinna理论 /
- 方程组 /
- 微分差分方程 /
- 亚纯解
Abstract: This article investigates some properties of meromorphic solutions of the type of system of differential-difference equations of the following form $\begin{eqnarray*}\begin{cases}f_1^n-p_1(z)f_2(z+c)=h_1(z), \ \\f_2^n-p_2(z)f_1(z+c)=h_2(z)\end{cases}\end{eqnarray*}$ where n ≥ 4, p1(z)、p2(z) are non-zero polynomials, and h1(z), h2(z) are entire functions. By using Nevanlinna theorem, we have obtained the solution of above equation is unique. We also discuss the conditions for several types of system of differential-difference equations if the systems of equations actually pose meromorphic solutions of finite order. -
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