Meromorphic solutions of a Riccati differential equation with a doubly periodic coefficient

We treat a Riccati differential equation w′+w2+p(z)=0, where p(z) is a nonconstant doubly periodic meromorphic function. Under certain assumptions, every solution is meromorphic in the whole complex plane. We show that the growth order of it is equal to 2, and examine the frequency of α-points and poles. Furthermore, the number of doubly periodic solutions is discussed.