A priori analysis of initial data for the Ricatti equation and asymptotic properties of
its solutions

Nina Chernyavskaya, Jeremy Schiff and Leonid Shuster

Bulletin of the London Mathematical Society 41 723-732 (2009).

We obtain two main results for the Cauchy problem
of a Riccati equation. We determine conditions under
which the solution can be extended to the whole of R
and study the asymptotic
properties of solutions as the argument tends to infinity.