论文标题
解决某些差异方程的解决方案的有效有限
Effective finiteness of solutions to certain differential and difference equations
论文作者
论文摘要
对于具有复杂系数的r（z，w），在w中至少为2的程度，我们表明有理函数f（z）求解差方程f（z+1）= r（z+1）= r（z，f（z））是有限的，并且仅在两个变量中的r度中以r的程度为单位。这补充了Yanagihara的结果，Yanagihara表明，对这种差异方程式的任何有限级杂型解决方案都必须是一个合理的函数。我们证明了基于Eremenko的结果的微分方程F'（z）= r（z，f（z））的相似结果。
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.
