Schwarzian微分方程的精确亚纯解
Exact meromorphic solutions of Schwarzian differential equations
摘要：
本文研究了自治Schwarzian微分方程的精确亚纯解。本文构造了Schwarzian微分方程六种典型类型中五种典型类型的全部超越亚纯解。特别地，四种类型的解被证明是椭圆函数。此外，所有的超越亚纯解是局部内射或具有皮卡德例外值的其余标准型的特点。
英文摘要：
This paper studies exact meromorphic solutions of the autonomous Schwarzian differential equations. All transcendental meromorphic solutions of five canonical types (among six) of the autonomous Schwarzian differential equations are constructed explicitly. In particular, the solutions of four types are shown to be elliptic functions. Also, all transcendental meromorphic solutions that are locally injective or possess a Picard exceptional value are characterized for the remaining canonical type.
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