Complex Variables 27:365-382 (1995)

© 1995 OPA (Overseas Publishers Association) Amsterdam B.V.

AMS 1991: 34A20

Abstract: Solutions of the Riccati equation W'+W ²= e ^2z are known to be asymptotic to e ^z or e ^-z. We show that those solutions which are asymptotic to e ^z have regular growth over C(e ^z) as z -> in funnel-like regions D between curves of the form y = ± K e ^{-x-2 e x}. Here the notion of regular growth over a differential field H of holomorphic germs on D is inspired by real Hardy field theory and is a generalization of the classical notion of non-oscillation. It means that for any differential polynomial P(X, X', ...) with coefficients in H, the function P(W, W', ...) is ultimately zero free in D or identically zero.

@article{dg:reg,author={Gokhman, D.},
title={Regular growth of solutions of the Riccati equation
$W'+W^2=e^{2z}$ in the complex plane},
journal={Complex Variables},volume={27},pages={365--382},year={1995}}