Doubly periodic solutions of the Riccati equation in complex domain (Q1203893)

In the beginning the existence of a global solution of a complex-valued Riccati equation of a single real independent variable is discussed by using stereographic projection. It is proved that if it is periodic it has at least one periodic solution. Then, the discussions are extended to the case of a single complex independent variable and the results are obtained when the coefficients of Riccati equations are doubly periodic. In this connection meta meromorphic functions and meta elliptic functions are defined.