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

N. A. Chernyavskaya; Jeremy Schiff; L. A. Shuster

doi:10.1112/blms/bdp050

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

N. A. Chernyavskaya
, Jeremy Schiff
, L. A. Shuster

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

We obtain two main results for the Cauchy problem where x0, y0 ∈ , r > 0, q ≥ 0, 1/r ∈ L₁^loc(), q ∈ L ₁^loc() 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.

Original language	English
Pages (from-to)	723-732
Number of pages	10
Journal	Bulletin of the London Mathematical Society
Volume	41
Issue number	4
DOIs	https://doi.org/10.1112/blms/bdp050
State	Published - 1 Jan 2009

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General Mathematics

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abstract = "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.",

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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.

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

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