Displaying similar documents to “On the existence of meromorphic solutions of differential equations having arbitarily rapid growth.”

On meromorphic solutions of the Riccati differential equations

Ran Ran Zhang, Zong Xuan Chen (2010)

Annales Polonici Mathematici

Similarity:

We investigate the growth and Borel exceptional values of meromorphic solutions of the Riccati differential equation w' = a(z) + b(z)w + w², where a(z) and b(z) are meromorphic functions. In particular, we correct a result of E. Hille [Ordinary Differential Equations in the Complex Domain, 1976] and get a precise estimate on the growth order of the transcendental meromorphic solution w(z); and if at least one of a(z) and b(z) is non-constant, then we...