Research of complex functional equations by means of theory of meromorphic functions

本文研究复平面上某些函数方程的亚纯解。得到了差分Riccati方程与二阶线性差分方程之间的一个关系，并研究了某些函数方程亚纯解的存在性和亚纯解的增长级.在此基础上，我们研究了小阶亚纯函数的性质。建立了Valiron-Mokhon'ko定理的一般形式。我们将这个结果应用到Schroder型函数方程。为了研究线性q-差分方程整体解的存在性，得到了整函数系数与增长阶之间的关系。

We are concerned with meromorphic solutions of some functional equations in the complex plane. We obtained a relation between difference Riccati equations and linear difference equations of second order, and also investigated the existence of meromorphic solutions to some functional equations and the order of growth of meromorphic solutions. Further, we considered the properties of meromorphic functions of small order. The general form of the Valiron-Mokhon’ko theorem is established. We applied this result to Schroder type functional equations. The relation between the coefficients of an entire function and the order of growth is obtained in order to investigate the existence of entire solution of linear q-difference equations.