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 -