一类微分和差分方程解的有效有限性
Effective finiteness of solutions to certain differential and difference equations
摘要：
对复系数有理函数R（z，w），证明了解差分方程f（z+1）=R（z，f（z））的有理函数f（z）的个数是有限的，且仅以R在两个变量中的次数为界.这补充了Yanagihara的一个结果，Yanagihara证明了这类差分方程的任何有限阶亚纯解必须是有理函数。我们证明了一个类似的结果微分方程f '（z）=R（z，f（z）），Eremenko的结果的基础上。
英文摘要：
For R(z, w) rational with complex coefficients, of degree at least 2 in w, we show that the number of rational functions f(z) solving the difference equation f(z+1)=R(z, f(z)) is finite and bounded just in terms of the degrees of R in the two variables. This complements a result of Yanagihara, who showed that any finite-order meromorphic solution to this sort of difference equation must be a rational function. We prove a similar result for the differential equation f'(z)=R(z, f(z)), building on a result of Eremenko.
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