一类Schwarzian微分方程的亚纯解  

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

作　　者：陆小庆 张建军 廖良文[2] LU Xiaoqing;ZHANG Jianjun;LIAO Liangwen(Mathematics and Information Technology School, Jiangsu Second Normal University,Nanjing Jiangsu 210013,China;Department of Mathematics, Nanjing University, Nanjing Jiangsu 210093,China)

机构地区：[1]江苏第二师范学院数学与信息技术学院,江苏南京210013 [2]南京大学数学系,江苏南京210093

出　　处：《江西师范大学学报（自然科学版）》2017年第6期585-590,共6页Journal of Jiangxi Normal University(Natural Science Edition)

基　　金：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

摘　　要：研究了如下形式的Schwarzian微分方程亚纯解的存在与结构问题:(f″/f')'-1/2(f″/f')=Pm(z)/Qn(z),其中Pm(z),Qn(z)是次数分别为m,n的不可约多项式,满足m≤n-2.已有研究结果给出了在该方程存在亚纯解时Pm(z)/Qn(z)的特征,涉及比较复杂的行列式运算.该文找到了替换行列式运算的新检验条件,通过判断有限个方程组是否有解来判断Schwarzian方程是否存在亚纯解,并给出了亚纯解的具体结构.In this paper,meromorphic solutions of the following type of the Schwarzian differential equation f″f′′-12f″f′2=P m(z)Q n(z)are studied.Here P m(z),Q n(z)are two irreducible polynomials of degree m,n satisfying m≤n-2.The characterization of P m(z)Q n(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.

关 键 词：Schwarzian微分方程 Mbius变换 亚纯解 

分 类 号：O174.52[理学—数学]