In this paper,we focus on the admissible transcendental meromorphic solutions of the following delay Schwarzian differential equations with rational coefficients f(z+1)-f(z-1)+a(z)S(f,z)=P(z,f(z))/Q(z,f(z)).We obtain ...In this paper,we focus on the admissible transcendental meromorphic solutions of the following delay Schwarzian differential equations with rational coefficients f(z+1)-f(z-1)+a(z)S(f,z)=P(z,f(z))/Q(z,f(z)).We obtain the necessary conditions on the degree of R(z,f)for these delay differential equations and give a classification of the delay Schwarzian differential equations according to the multiplicities of the root of Q(z,f)on f.Finally,we provide some examples to illustrate that all cases occur.展开更多
基金supported by the National Natural Science Foundation of China(12201420,12231013,11701382 and 11971288)the Guangdong Basic and Applied Basic Research Foundation,China(2021A1515010054)and NCAMS.
文摘In this paper,we focus on the admissible transcendental meromorphic solutions of the following delay Schwarzian differential equations with rational coefficients f(z+1)-f(z-1)+a(z)S(f,z)=P(z,f(z))/Q(z,f(z)).We obtain the necessary conditions on the degree of R(z,f)for these delay differential equations and give a classification of the delay Schwarzian differential equations according to the multiplicities of the root of Q(z,f)on f.Finally,we provide some examples to illustrate that all cases occur.
