Classification of initial data for the Riccati equation

N. Chernyavskaya; L. Shuster

Classification of initial data for the Riccati equation

N. Chernyavskaya
, L. Shuster

Department of Mathematics

Ben-Gurion University of the Negev

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

6 Scopus citations

Abstract

We consider a Cauchy problem y′(x)+y²(x)=q(x), y(x)\_{x= x0}=y₀ where x₀,y₀∈R e q(x) ∈ L₁^loc(R) is a non-negative function satisfying the condition: ∫^x _-∞ q(t) dt > 0, ∫^∞_x q(t) dt > 0 for x ∈ R. We obtain the conditions under which y(x) can be continued to all of R. This depends on x₀, y₀ and the properties of q(x).

Original language	English
Pages (from-to)	511-525
Number of pages	15
Journal	Bollettino della Unione Matematica Italiana B
Volume	5
Issue number	2
State	Published - Jun 2002

Cite this

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title = "Classification of initial data for the Riccati equation",

abstract = "We consider a Cauchy problem y′(x)+y2(x)=q(x), y(x)\textbackslash{}x= x0=y0 where x0,y0∈R e q(x) ∈ L1loc(R) is a non-negative function satisfying the condition: ∫x -∞ q(t) dt > 0, ∫∞x q(t) dt > 0 for x ∈ R. We obtain the conditions under which y(x) can be continued to all of R. This depends on x0, y0 and the properties of q(x).",

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N2 - We consider a Cauchy problem y′(x)+y2(x)=q(x), y(x)\x= x0=y0 where x0,y0∈R e q(x) ∈ L1loc(R) is a non-negative function satisfying the condition: ∫x -∞ q(t) dt > 0, ∫∞x q(t) dt > 0 for x ∈ R. We obtain the conditions under which y(x) can be continued to all of R. This depends on x0, y0 and the properties of q(x).

AB - We consider a Cauchy problem y′(x)+y2(x)=q(x), y(x)\x= x0=y0 where x0,y0∈R e q(x) ∈ L1loc(R) is a non-negative function satisfying the condition: ∫x -∞ q(t) dt > 0, ∫∞x q(t) dt > 0 for x ∈ R. We obtain the conditions under which y(x) can be continued to all of R. This depends on x0, y0 and the properties of q(x).

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AN - SCOPUS:0042735173

SN - 0392-4041

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JO - Bollettino della Unione Matematica Italiana B

JF - Bollettino della Unione Matematica Italiana B

IS - 2

ER -

Classification of initial data for the Riccati equation

Abstract

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