| Summary: | 碩士 === 國立政治大學 === 應用數學研究所 === 98 === In this thesis, we use the theory of value distribution to study the existence of solution of the following functional equation:
\[\sum_{j=1}^pa_j(z)f_j(z)^{k_j}=1,\]
where $a_1(z),\cdots ,a_p(z)$ are meromorphic functions. For some special case, new and old examples of the solutions are given. For the general case, a necessary condition for the existence of solution is considered. Moreover, we obtain a result on the distribution of zeros and poles of a class of meromorphic functions.
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