TY - JOUR
T1 - A priori analysis of initial data for the Riccati equation and asymptotic properties of its solutions
AU - Chernyavskaya, N. A.
AU - Schiff, Jeremy
AU - Shuster, L. A.
PY - 2009/1/1
Y1 - 2009/1/1
N2 - We obtain two main results for the Cauchy problem where x0, y0 ∈ , r > 0, q ≥ 0, 1/r ∈ L1loc(), q ∈ L 1loc() and(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 . (2) When the solution is defined on an infinite interval, we study its asymptotic properties as the argument tends to infinity.
AB - We obtain two main results for the Cauchy problem where x0, y0 ∈ , r > 0, q ≥ 0, 1/r ∈ L1loc(), q ∈ L 1loc() and(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 . (2) When the solution is defined on an infinite interval, we study its asymptotic properties as the argument tends to infinity.
UR - http://www.scopus.com/inward/record.url?scp=68449085621&partnerID=8YFLogxK
U2 - 10.1112/blms/bdp050
DO - 10.1112/blms/bdp050
M3 - Article
AN - SCOPUS:68449085621
SN - 0024-6093
VL - 41
SP - 723
EP - 732
JO - Bulletin of the London Mathematical Society
JF - Bulletin of the London Mathematical Society
IS - 4
ER -