## The Meromorphic Solutions of a Certain Type of the Schwarzian Differential Equation

**LU Xiaoqing;ZHANG Jianjun;LIAO Liangwen;Mathematics and Information Technology School,Jiangsu Second Normal University;Department of Mathematics,Nanjing University;**

In this paper,meromorphic solutions of the following type of the Schwarzian differential equation (f″/f')'-1/2(f″/f')=Pm(z)/Qn(z) are studied. Here Pm( z),Qn( z) are two irreducible polynomials of degree m,n satisfying m≤n-2. The characterization of Pm( z) /Qn( z) for ensuring the existence of meromorphic solutions is known,but very complicated in the calculation of determinants. A new condition,which tests the existence of solutions of a series of equation sets,has been found in this paper,to replace the determinant requirements. Furthermore,the solution structures are also given out for the first time.

【Fund】：
国家自然科学基金(11671191 11271179);;
江苏省自然科学基金(BK20140767);;
江苏省"青蓝工程"资助项目

【CateGory Index】： O174.52;O175

【CateGory Index】： O174.52;O175

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