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Bulletin of the London Mathematical Society Advance Access published online on July 3, 2009
Bulletin of the London Mathematical Society, doi:10.1112/blms/bdp050
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© 2009 London Mathematical Society

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

N. A. Chernyavskaya

Department of Mathematics and Computer Science
Ben-Gurion University of the Negev
P.O.B. 653
Beer-Sheva 84105
Israel
nina@cs.bgu.ac.il

Jeremy Schiff

Department of Mathematics
Bar-Ilan University
Ramat Gan 52900
Israel
schiff@math.biu.ac.il

L. A. Shuster

Department of Mathematics
Bar-Ilan University
Ramat Gan 52900
Israel

Received 20 August 2008. Revision received 5 March 2009.

We obtain two main results for the Cauchy problem


Formula

where x0, y0 isin R, r > 0, q ≥ 0, 1/r isin LFormula(R), q isin LFormula(R) and


Formula

(1) For given initial data x0, y0 and functions r and q, we give a condition that can be used to determine whether the solution of the problem can be continued to the whole of R. (2) When the solution is defined on an infinite interval, we study its asymptotic properties as the argument tends to infinity.

2000 Mathematics Subject Classification 34A34.


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