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.